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Fractional stochastic wave equation driven by a Gaussian noise rough in spaceApr 22 2019In this article, we consider fractional stochastic wave equations on $\mathbb R$ driven by a multiplicative Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst parameter $H\in(\frac14, \frac12)$ ... More

Existence and regularity of pre-invariant measures, transition functions and time homogeneous Itô-SDEsApr 22 2019We show existence of a pre-invariant measure $m$ for a large class of divergence and non-divergence form elliptic second order partial differential operators with locally Sobolev regular diffusion coefficient and locally square integrable drift. Subsequently, ... More

Prediction Law of Mixed Gaussian Volterra ProcessesApr 22 2019We study the regular conditional law of mixed Gaussian Volterra processes under the influence of model disturbances. More precisely, we study prediction of Gaussian Volterra processes driven by a Brownian motion in a case where the Brownian motion is ... More

On asymptotic structure of the critical Galton-Watson Branching Processes with infinite variance and ImmigrationApr 22 2019We observe the Galton-Watson Branching Processes. Limit properties of transition functions and their convergence to invariant measures are investigated.

On matrix product ansatz for Asymmetric Simple Exclusion Process with open boundary in the singular caseApr 21 2019We study a substitute for the matrix product ansatz for Asymmetric Simple Exclusion Process with open boundary in the ``singular case'' $\alpha\beta=q^N\gamma\delta$, when the standard form of the matrix product ansatz of Derrida, Evans, Hakim and Pasquier ... More

Auditable Blockchain Randomization ToolApr 20 2019Randomization is an integral part of well-designed statistical trials, and is also a required procedure in legal systems, see Marcondes et al. (2019) This paper presents an easy to implement randomization protocol that assures, in a formal mathematical ... More

Comparison of discrete and continuum Liouville first passage percolationApr 19 2019Discrete and continuum Liouville first passage percolation (DLFPP, LFPP) are two approximations of the conjectural $\gamma$-Liouville quantum gravity (LQG) metric, obtained by exponentiating the discrete Gaussian free field (GFF) and the circle average ... More

Magnetization in the zig-zag layered Ising model and orthogonal polynomialsApr 19 2019We discuss the magnetization $M_m$ in the $m$-th column of the zig-zag layered 2D Ising model on a half-plane using Kadanoff-Ceva fermions and orthogonal polynomials techniques. Our main result gives an explicit representation of $M_m$ via $m\times m$ ... More

Universality for critical kinetically constrained models: infinite number of stable directionsApr 19 2019Kinetically constrained models (KCM) are reversible interacting particle systems on $\mathbb{Z}^d$ with continuous-time constrained Glauber dynamics. They are a natural non-monotone stochastic version of the family of cellular automata with random initial ... More

On Markovian semigroups of Lévy driven SDEs, symbols and pseudo--differential operatorsApr 19 2019We analyse analytic properties of nonlocal transition semigroups associated with a class of stochastic differential equations (SDEs) in $\mathbb{R}^d$ driven by pure jump--type L\'evy processes. First, we will show under which conditions the semigroup ... More

The Effect of Recombination on the Speed of EvolutionApr 18 2019It has been a puzzling question why some organisms reproduce sexually. Fisher and Muller hypothesized that reproducing by sex can speed up the evolution. They explained that in the sexual reproduction, recombination can combine beneficial alleles that ... More

The stochastic thin-film equation: existence of nonnegative martingale solutionsApr 18 2019We consider the stochastic thin-film equation with colored Gaussian Stratonovich noise and establish the existence of nonnegative weak (martingale) solutions. The construction is based on a Trotter-Kato-type decomposition into a deterministic and a stochastic ... More

The acceptance profile of invasion percolation at $p_c$ in two dimensionsApr 18 2019Invasion percolation is a stochastic growth model that follows a greedy algorithm. After assigning i.i.d. uniform random variables (weights) to all edges of $\mathbb{Z}^d$, the growth starts at the origin. At each step, we adjoin to the current cluster ... More

Breaking of 1RSB in random MAX-NAE-SATApr 18 2019For several models of random constraint satisfaction problems, it was conjectured by physicists and later proved that a sharp satisfiability transition occurs. For random $k$-SAT and related models it happens at clause density $\alpha$ around $2^k$. Just ... More

On discrete-time self-similar processes with stationary incrementsApr 18 2019In this paper we study the self-similar processes with stationary increments in a discrete-time setting. Different from the continuous-time case, it is shown that the scaling function of such a process may not take the form of a power function $b(a)=a^H$. ... More

Phase transition in the exclusion process on the Sierpinski gasket with slowed boundary reservoirsApr 18 2019We derive the macroscopic laws that govern the evolution of the density of particles in the exclusion process evolving on the Sierpinski gasket in the presence of a slow boundary. Depending on the slowness of the boundary we obtain, at the hydrodynamics ... More

Limiting entry times distribution for arbitrary null sets SETSApr 18 2019We describe an approach that allows us to deduce the limiting return times distribution for arbitrary sets to be compound Poisson distributed. We establish a relation between the limiting return times distribution and the probability of the cluster sizes, ... More

Local semicircle law under fourth moment conditionApr 18 2019We consider a random symmetric matrix ${\bf X} = [X_{jk}]_{j,k=1}^n$ with upper triangular entries being independent random variables with mean zero and unit variance. Assuming that $\max_{jk} {\mathbb E} |X_{jk}|^{4+\delta} < \infty, \delta > 0$, it ... More

A strong order $3/4$ method for SDEs with discontinuous drift coefficientApr 18 2019In this paper we study strong approximation of the solution of a scalar stochastic differential equation (SDE) at the final time in the case when the drift coefficient may have discontinuities in space. Recently it has been shown in [M\"uller-Gronbach, ... More

Convergence of metadynamics: discussion of the adiabatic hypothesisApr 18 2019By drawing a parallel between metadynamics and self interacting models for polymers, we study the longtime convergence of the original metadynamics algorithm in the adiabatic setting, namely when the dynamics along the collective variables decouples from ... More

Exponential Quadratic BSDEs with infinite activity JumpsApr 18 2019In this paper, we study a Backward Stochastic Differential Equation with Jumps (BSDEJs in short) where the jumps have infinite activity. Following a forward approach based on Exponential Quadratic semimartingale, we prove the existence of solution of ... More

Stochastic approximation of quasi-stationary distributions for diffusion processes in a bounded domainApr 18 2019We study a random process with reinforcement, which evolves following the dynamics of a given diffusion process in a bounded domain and is resampled according to its occupation measure when it reaches the boundary. We show that its occupation measure ... More

Practical criteria for R-positive recurrence of unbounded semigroupsApr 18 2019The goal of this note is to show how recent results on the theory of quasi-stationary distributions allow to deduce effortlessly general criteria for the geometric convergence of normalized unbounded semigroups.

Stable recovery and the coordinate small-ball behaviour of random vectorsApr 17 2019Recovery procedures in various application in Data Science are based on \emph{stable point separation}. In its simplest form, stable point separation implies that if $f$ is "far away" from $0$, and one is given a random sample $(f(Z_i))_{i=1}^m$ where ... More

Complete convergence theorem for a two level contact processApr 17 2019We study a two-level contact process. We think of fleas living on a species of animals. The animals are a supercritical contact process in $\mathbb{Z}^d$. The contact process acts as the random environment for the fleas. The fleas do not affect the animals, ... More

Information and Memory in Dynamic Resource AllocationApr 17 2019We propose a general framework, dubbed Stochastic Processing under Imperfect Information (SPII), to study the impact of information constraints and memories on dynamic resource allocation. The framework involves a Stochastic Processing Network (SPN) scheduling ... More

The evolution to equilibrium of solutions to nonlinear Fokker-Planck equationApr 17 2019One proves the $H$-theorem for mild solutions to a nondegenerate, nonlinear Fokker-Planck equation $$ u_t-\Delta\beta(u)+\mathrm{ div}(D(x)b(u)u)=0, \ t\ge0, \ x\in\mathbb{R}^d,\hspace{1cm} (1)$$ and under appropriate hypotheses on $\beta,$ $D$ and $b$ ... More

Higher dimensional connectivity and minimal degree of random graphs with an eye towards minimal free resolutionsApr 17 2019In this note we define and study graph invariants generalizing to higher dimension the maximum degree of a vertex and the vertex-connectivity (our $0$-dimensional cases). These are known to coincide almost surely in any regime for Erdoes-Renyi random ... More

Upper tails via high moments and entropic stabilityApr 17 2019Suppose that $X$ is a bounded-degree polynomial with nonnegative coefficients on the $p$-biased discrete hypercube. Our main result gives sharp estimates on the logarithmic upper tail probability of $X$ whenever an associated extremal problem satisfies ... More

Restricted hypercontractivity on the Poisson spaceApr 17 2019We show that the Ornstein-Uhlenbeck semigroup associated with a general Poisson random measure is hypercontractive, whenever it is restricted to non-increasing mappings on configuration spaces. We deduce from this result some versions of Talagrand's $L^1$-$L^2$ ... More

The Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan]Apr 17 2019This is the text to accompany my Bourbaki seminar from 30th March 2019, on the maximum size of the Riemann zeta function in "almost all" intervals of length 1 on the critical line. It surveys the conjecture of Fyodorov--Hiary--Keating on the behaviour ... More

The Long ans Short Time Asymptotics of the Two-Time Distribution in Local Random GrowthApr 17 2019The two-time distribution gives the limiting joint distribution of the heights at two different times of a local 1D random growth model in the curved geometry. This distribution has been computed in a specific model but is expected to be universal in ... More

A microscopic derivation of Gibbs measures for nonlinear Schrödinger equations with unbounded interaction potentialsApr 17 2019We study the derivation of the Gibbs measure for the nonlinear Schr\"{o}dinger equation (NLS) from many-body quantum thermal states in the high-temperature limit. In this paper, we consider the nonlocal NLS with defocusing and unbounded $L^p$ interaction ... More

Existence of Geometric Ergodic Periodic Measures of Stochastic Differential EquationsApr 17 2019Periodic measures are the time-periodic counterpart to invariant measures for dynamical systems and can be used to characterise the long-term periodic behaviour of stochastic systems. This paper gives sufficient conditions for the existence, uniqueness ... More

Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation modelsApr 17 2019We use a conditional Karhunen-Lo\`eve (KL) model to quantify and reduce uncertainty in a stochastic partial differential equation (SPDE) problem with partially-known space-dependent coefficient, $Y(x)$. We assume that a small number of $Y(x)$ measurements ... More

Remarks on the Rényi Entropy of a sum of IID random variablesApr 17 2019In this note we study a conjecture of Madiman and Wang which predicted that the generalized Gaussian distribution minimizes the R\'{e}nyi entropy of the sum of independent random variables. Through a variational analysis, we show that the generalized ... More

Optimal loss-carry-forward taxation for Lévy risk processes stopped at general draw-down timeApr 17 2019Motivated by Kyprianou and Zhou (2009), Wang and Hu (2012), Avram et al. (2017), Li et al. (2017) and Wang and Zhou (2018), we consider in this paper the problem of maximizing the expected accumulated discounted tax payments of an insurance company, whose ... More

Tightness of Liouville first passage percolation for $γ\in (0,2)$Apr 16 2019We study Liouville first passage percolation metrics associated to a Gaussian free field $h$ mollified by the two-dimensional heat kernel $p_t$ in the bulk, and related star-scale invariant metrics. For $\gamma \in (0,2)$ and $\xi = \frac{\gamma}{d_{\gamma}}$, ... More

Outliers in spectrum of sparse Wigner matricesApr 16 2019In this paper, we study the effect of sparsity on the appearance of outliers in the semi-circular law. Let $(W_n)_{n=1}^\infty$ be a sequence of random symmetric matrices such that each $W_n$ is $n\times n$ with i.i.d entries above and on the main diagonal ... More

On the Convergence of Random Tridiagonal Matrices to Stochastic SemigroupsApr 16 2019We develop an improved version of the stochastic semigroup approach to study the edge of $\beta$-ensembles pioneered by Gorin and Shkolnikov, and later extended to rank-one additive perturbations by the author and Shkolnikov. Our method is applicable ... More

Stochastic nonlinear Fokker-Planck equationsApr 16 2019The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker-Planck equations is proven. This type of stochastic PDE is shown to arise in the mean field limit of weakly interacting diffusions with common noise. The ... More

The Euler-Maruyama Scheme for SDEs with Irregular Drift: Convergence Rates via Reduction to a Quadrature ProblemApr 16 2019We study the strong convergence order of the Euler-Maruyama scheme for scalar stochastic differential equations with additive noise and irregular drift. We provide a novel framework for the error analysis by reducing it to a weighted quadrature problem ... More

Final solution to the problem of relating a true copula to an imprecise copulaApr 16 2019In this paper we solve in the negative the problem proposed in this journal (I. Montes et al., Sklar's theorem in an imprecise setting, Fuzzy Sets and Systems, 278 (2015), 48-66) whether an order interval defined by an imprecise copula contains a copula. ... More

Large deviation for uniform graphs with given degreesApr 16 2019Consider the random graph sampled uniformly from the set of all simple graphs with a given degree sequence. Under mild conditions on the degrees, we establish a Large Deviation Principle (LDP) for these random graphs, viewed as elements of the graphon ... More

Inequalities for m-Divisible Distributions and Testing of Infinite DivisibilityApr 16 2019We state some inequalities for m-divisible and infinite divisible characteristic functions. Basing on them we propose a statistical test for a distribution to be infinitely divisible. Keywords: infinite divisible distributions; statistical tests.

Continued fractions, the Chen-Stein method and extreme value theoryApr 16 2019In this paper, we investigate extreme value theory in the context of continued fractions using the Chen-Stein method. We give an upper bound for the rate of convergence in the Doeblin-Iosifescu asymptotics for the exceedances and deduce several consequences. ... More

On the Spectrum of Self--Adjoint Lévy GeneratorsApr 16 2019We investigate the spectrum of the generator of a self-adjoint transition semigroup of a (symmetric) L\'{e}vy process taking values in $d$--dimensional space.

Non-integrable dimers: Universal fluctuations of tilted height profilesApr 16 2019We study a class of close-packed dimer models on the square lattice, in the presence of small but extensive perturbations that make them non-determinantal. Examples include the 6-vertex model close to the free-fermion point, and the dimer model with plaquette ... More

Biased random walk conditioned on survival among Bernoulli obstacles: subcritical phaseApr 16 2019We consider a discrete time biased random walk conditioned to avoid Bernoulli obstacles on ${\mathbb Z}^d$ ($d\geq 2$) up to time $N$. This model is known to undergo a phase transition: for a large bias, the walk is ballistic whereas for a small bias, ... More

Maximal displacement of simple random walk bridge on Galton-Watson treesApr 16 2019We analyze simple random walk on a supercritical Galton-Watson tree, where the walk is conditioned to return to the root at time $2n$. Specifically, we establish the asymptotic order (up to a constant factor) as $n\to\infty$, of the maximal displacement ... More

Fractional Laplacian with Hardy drift via desingularizing weightsApr 15 2019We establish the weighted Nash initial estimate for the heat kernel of the fractional Laplacian, perturbed by a drift having a critical-order singularity, using the method of desingularizing weights.

Local times for continuous paths of arbitrary regularityApr 15 2019We study a pathwise continuous local time of order p for functions with finite p-th variation along a sequence of time partitions, for even integers p greater than or equal to 2. With this notion, we establish a Tanaka-type change of variable formula, ... More

Limit theorems for U-statistics of Bernoulli dataApr 15 2019In this paper, we consider U-statistics whose data is a strictly stationary sequence which can be expressed as a functional of an i.i.d. one. We establish a strong law of large numbers, a bounded law of the iterated logarithms and a central limit theorem ... More

A monotone scheme for G-equations with application to the convergence rate of robust central limit theoremApr 15 2019We propose a monotone approximation scheme for a class of fully nonlinear PDEs called G-equations. Such equations arise often in the characterization of G-distributed random variables in a sublinear expectation space. The proposed scheme is constructed ... More

Coarse-graining Molecular Systems by Spectral MatchingApr 15 2019Coarse-graining has become an area of tremendous importance within many different research fields. For molecular simulation, coarse-graining bears the promise of finding simplified models such that long-time simulations of large-scale systems become computationally ... More

The Landscape of the Planted Clique Problem: Dense subgraphs and the Overlap Gap PropertyApr 15 2019In this paper we study the computational-statistical gap of the planted clique problem, where a clique of size $k$ is planted in an Erdos Renyi graph $G(n,\frac{1}{2})$ resulting in a graph $G\left(n,\frac{1}{2},k\right)$. The goal is to recover the planted ... More

Bulk eigenvalue fluctuations of sparse random matricesApr 15 2019We consider a class of sparse random matrices, which includes the adjacency matrix of Erd\H{o}s-R\'enyi graphs $\mathcal G(N,p)$ for $p \in [N^{\varepsilon-1},N^{-\varepsilon}]$. We identify the joint limiting distributions of the eigenvalues away from ... More

A decorated tree approach to random permutations in substitution-closed classesApr 15 2019We establish a novel bijective encoding that represents permutations as forests of decorated (or enriched) trees. This allows us to prove local convergence of uniform random permutations from substitution-closed classes satisfying a criticality constraint. ... More

Geometry of weighted recursive and affine preferential attachment treesApr 15 2019We study two models of growing recursive trees. For both models, initially the tree only contains one vertex $u_1$ and at each time $n\geq 2$ a new vertex $u_n$ is added to the tree and its parent is chosen randomly according to some rule. In the \emph{weighted ... More

Subgeometric ergodicity and $β$-mixingApr 15 2019Apr 16 2019It is well known that stationary geometrically ergodic Markov chains are $\beta$-mixing (absolutely regular) with geometrically decaying mixing coefficients. Furthermore, for initial distributions other than the stationary one, geometric ergodicity implies ... More

Subgeometric ergodicity and $β$-mixingApr 15 2019It is well known that stationary geometrically ergodic Markov chains are $\beta$-mixing (absolutely regular) with geometrically decaying mixing coefficients. Furthermore, for initial distributions other than the stationary one, geometric ergodicity implies ... More

Subgeometrically ergodic autoregressionsApr 15 2019In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study the stability of nonlinear time series models. Subgeometric ergodicity means that the transition probability measures converge to the stationary ... More

Subgeometrically ergodic autoregressionsApr 15 2019Apr 16 2019In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study the stability of nonlinear time series models. Subgeometric ergodicity means that the transition probability measures converge to the stationary ... More

Donsker's theorem in {Wasserstein}-1 distanceApr 15 2019We compute the Wassertein-1 (or Kolmogorov-Rubinstein) distance between a random walk in $R^d$ and the Brownian motion. The proof is based on a new estimate of the Lipschitz modulus of the solution of the Stein's equation. As an application, we can evaluate ... More

Making multigraphs simple by a sequence of double edge swapsApr 15 2019A double edge swap is an operation on (undirected) loopy multigraphs (multiple edges and multiple loops are allowed) that replaces two edges $(v_1,v_2)$ and $(v_3,v_4)$ by $(v_2,v_3)$ and $(v_4,v_1)$. The swap is admissible if $(v_1,v_2)$ and $(v_3,v_4)$ ... More

An optimal polynomial approximation of Brownian motionApr 15 2019In this paper, we will present a strong (or pathwise) approximation of standard Brownian motion by a class of orthogonal polynomials. Remarkably the coefficients obtained from the expansion of Brownian motion in this polynomial basis are independent Gaussian ... More

Mean field limits for interacting Hawkes processes in a diffusive regimeApr 15 2019Apr 17 2019We consider a sequence of systems of Hawkes processes having mean field interactions in a diffusive regime. The stochastic intensity of each process is a solution of a stochastic differential equation driven by N independent Poisson random measures. We ... More

Mean field limits for interacting Hawkes processes in a diffusive regimeApr 15 2019We consider a sequence of systems of Hawkes processes having mean field interactions in a diffusive regime. The stochastic intensity of each process is a solution of a stochastic differential equation driven by N independent Poisson random measures. We ... More

Tail probabilities of random linear functions of regularly varying random vectorsApr 15 2019We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$ under random ... More

Some remarks about the maximal perimeter of convex sets with respect to probability measuresApr 15 2019In this note we study the maximal perimeter of a convex set in $\mathbb{R}^n$ with respect to various classes of measures. Firstly, we show that for a probability measure $\mu$ on $ \mathbb{R}^n$, satisfying very mild assumptions, there exists a convex ... More

Ergodicity and Feyman-Kac Formula for Space-Distribution Valued Diffusion ProcessesApr 15 2019Apr 16 2019Let $\mathcal P_2$ be the space of probability measures $\mu$ on $\mathbb R^d$ with $\mu(|\cdot|^2)<\infty$. Consider the following time-dependent second order differential operator on $\mathbb R^d\times\mathcal P_2:$ $${\bf L}_t f (x,\mu):= \frac 1 2\big\<\bar ... More

Ergodicity and Feyman-Kac Formula for Space-Distribution Valued Diffusion ProcessesApr 15 2019Let $\mathcal P_2$ be the space of probability measures $\mu$ on $\mathbb R^d$ with $\mu(|\cdot|^2)<\infty$. Consider the following time-dependent second order differential operator on $\mathbb R^d\times\mathcal P_2:$ $${\bf L}_t f (x,\mu):= \frac 1 2\big\<\bar ... More

Probabilistic local well-posedness of the cubic nonlinear wave equation in negative Sobolev spacesApr 15 2019We study the three-dimensional cubic nonlinear wave equation (NLW) with random initial data below $L^2(\mathbb{T}^3)$. By considering the second order expansion in terms of the random linear solution, we prove almost sure local well-posedness of the renormalized ... More

Rejection Sampling for General Tempered Stable Ornstein-Uhlenbeck ProcessesApr 15 2019We give an explicit representation for the transition law of a tempered stable Ornstein-Uhlenbeck process and use it to develop an accept-reject algorithm for exact simulation of increments from this process. Our results apply to general classes of both ... More

First passage time for Slepian process with linear barrierApr 14 2019In this paper we extend results of L.A. Shepp by finding explicit formulas for the first passage probability $F_{a,b}(T\, |\, x)={\rm Pr}(S(t)<a+bt \text{ for all } t\in[0,T]\,\, | \,\,S(0)=x)$, for all $T>0$, where $S(t)$ is a Gaussian process with mean ... More

On asymptotic normality of U-statistic of a stationary absolutely regular sequence in a triangular array schemeApr 14 2019Let $(X_{n,t})_{t=1}^{\infty}$ be a stationary absolutely regular sequence of real random variables with the distribution dependent on the number~$n$. The paper presents the sufficient conditions for the asymptotic normality (for $n\to\infty$ and common ... More

On asymptotic normality of U-statistic of a stationary absolutely regular sequence in a triangular array schemeApr 14 2019Apr 16 2019Let $(X_{n,t})_{t=1}^{\infty}$ be a stationary absolutely regular sequence of real random variables with the distribution dependent on the number~$n$. The paper presents the sufficient conditions for the asymptotic normality (for $n\to\infty$ and common ... More

Solvers and precondtioners based on Gauss-Seidel and Jacobi algorithms for non-symmetric stochastic Galerkin system of equationsApr 13 2019In this work, solvers and preconditioners based on Gauss-Seidel and Jacobi algorithms are explored for stochastic Galerkin discretization of partial differential equations (PDEs) with random input data. Gauss-Seidel and Jacobi algorithms are formulated ... More

Generalized Stochastic areas and windings arising from Anti-de Sitter and Hopf fibrationsApr 13 2019In the first part of this paper, we derive explicit expressions of the semi-group densities of generalized stochastic areas arising from the Anti-de Sitter and the Hopf fibrations. Motivated by the number-theoretical connection between the Heisenberg ... More

Concentration and Poincaré type inequalities for a degenerate pure jump Markov processApr 12 2019We study Talagrand concentration and Poincar\'e type inequalities for unbounded pure jump Markov processes. In particular we focus on processes with degenerate jumps that depend on the past of the whole system, based on the model introduced by Galves ... More

Mean-field backward-forward stochastic differential equations and nonzero sum stochastic differential gamesApr 12 2019We study a general class of fully coupled backward-forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the non-degeneracy ... More

Surface energy and boundary layers for a chain of atoms at low temperatureApr 12 2019We analyze the surface energy and boundary layers for a chain of atoms at low temperature for an interaction potential of Lennard-Jones type. The pressure (stress) is assumed small but positive and bounded away from zero, while the temperature $\beta^{-1}$ ... More

Zooming-in on a Lévy process: Failure to observe threshold exceedance over a dense gridApr 12 2019For a L\'evy process $X$ on a finite time interval consider the probability that it exceeds some fixed threshold $x>0$ while staying below $x$ at the points of a regular grid. We establish exact asymptotic behavior of this probability as the number of ... More

Strong Convergence of Infinite Color Balanced Urns Under Uniform ErgodicityApr 12 2019We consider the generalization of the P\'olya urn scheme with possibly infinite many colors as introduced in \cite{Th-Thesis, BaTH2014, BaTh2016, BaTh2017}. For countable many colors, we prove almost sure convergence of the urn configuration under \emph{uniform ... More

Double hypergeometric Lévy processes and self-similarityApr 12 2019Motivated by a recent paper of Budd, where a new family of positive self-similar Markov processes associated to stable processes appears, we introduce a new family of L\'evy processes, called the double hypergeometric class, whose Wiener-Hopf factorisation ... More

A Berry-Esseén theorem for partial sums of functionals of heavy-tailed moving averagesApr 12 2019In this paper we obtain Berry-Esse\'en bounds on partial sums of functionals of heavy-tailed moving averages, including the linear fractional stable noise, stable fractional ARIMA processes and stable Ornstein-Uhlenbeck processes. Our rates are obtained ... More

Exponential ergodicity for diffusions with jumps driven by a Hawkes processApr 12 2019In this paper, we introduce a new class of processes which are diffusions with jumps, where the jumps are driven by a multivariate linear Hawkes process, and study their long-time behavior. In the case of exponential memory kernels for the underlying ... More

The Lanczos Algorithm Under Few Iterations: Concentration and Location of the Ritz ValuesApr 12 2019We study the Lanczos algorithm where the initial vector is sampled uniformly from $\mathbb{S}^{n-1}$. Let $A$ be an $n \times n$ Hermitian matrix. We show that when run for few iterations, the output of the algorithm on $A$ is almost deterministic. For ... More

Community Detection in the Sparse Hypergraph Stochastic Block ModelApr 11 2019We consider the community detection problem in sparse random hypergraphs. Angelini et al. (2015) conjectured the existence of a sharp threshold on model parameters for community detection in sparse hypergraphs generated by a hypergraph stochastic block ... More

Skeletal stochastic differential equations for superprocessesApr 11 2019Apr 16 2019It is well understood that a supercritical superprocess is equal in law to a discrete Markov branching process whose genealogy is dressed in a Poissonian way with immigration which initiates subcritial superprocesses. The Markov branching process corresponds ... More

On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial valuesApr 11 2019Recently in [M. Hairer, M. Hutzenthaler, and A. Jentzen, Ann. Probab. 43, 2 (2015), 468--527] and [A. Jentzen, T. M\"uller-Gronbach, and L. Yaroslavtseva, Commun. Math. Sci. 14, 6 (2016), 1477--1500] stochastic differential equations (SDEs) with smooth ... More

The distribution of age-of-information performance measures for message processing systemsApr 11 2019The idea behind the recently introduced "age of information" performance measure of a networked message processing system is that it indicates our knowledge regarding the "freshness" of the most recent piece of information that can be used as a criterion ... More

The $L^2$ boundedness condition in nonamenable percolationApr 11 2019Let $G=(V,E)$ be a connected, locally finite, transitive graph, and consider Bernoulli bond percolation on $G$. In recent work, we conjectured that if $G$ is nonamenable then the matrix of critical connection probabilities $T_{p_c}(u,v)=\mathbb{P}_{p_c}(u\leftrightarrow ... More

CLT for the capacity of the range of stable random walksApr 11 2019In this article, we establish a central limit theorem for the capacity of the range process for a class of $d$-dimensional symmetric $\alpha$-stable random walks with the index satisfying $d\ge3\alpha$. Our approach is based on controlling the limit behavior ... More

The distribution function of a probability measure on a linearly ordered topological spaceApr 11 2019In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case. Moreover, we define ... More

On maximum of Gaussian random field having unique maximum point of its varianceApr 11 2019Gaussian random fields on Euclidean spaces whose variances reach their maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximum of theirs trajectories have been evaluated using Double Sum Method ... More

Pollicott's Algorithm for Markovian Products of Positive MatricesApr 11 2019In \cite{Pollicott}, M. Policott proposed an efficient algorithm, applying Ruelle's theory of transfer operators and Grothendieck's classical work on nuclear operators, to compute the Lyapunov exponent associated with the i.i.d. products of positive matrices. ... More

Theory of Cryptocurrency Interest RatesApr 10 2019A term structure model in which the short rate is zero is developed as a candidate for a theory of cryptocurrency interest rates. The price processes of crypto discount bonds are worked out, along with expressions for the instantaneous forward rates and ... More

Regularized divergences between covariance operators and Gaussian measures on Hilbert spacesApr 10 2019This work presents an infinite-dimensional generalization of the correspondence between the Kullback-Leibler and R\'enyi divergences between Gaussian measures on Euclidean space and the Alpha Log-Determinant divergences between symmetric, positive definite ... More

Ground States And Hyperuniformity Of The Hierarchical Coulomb Gas In All DimensionsApr 10 2019Large ensembles of points with Coulomb interactions arise in various settings of statistical mechanics, random matrices and optimization problems. Often such systems due to their natural repulsion exhibit remarkable hyperuniformity properties, that is, ... More