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Intersection times for critical branching random walkAug 22 2019We show that for a sequence of reversible Markov chains, the mixing-times are of smaller order than the maximal hitting times $t_{\mathrm{hit}}^{(n)}$ iff the product of the spectral-gap $\mathrm{gap}^{(n)}$ and $t_{\mathrm{hit}}^{(n)}$ diverges. This ... More
Rayleigh Random Flights on the Poisson line SIRSNAug 22 2019This paper reports a study of scale-invariant Rayleigh Random Flights ("RRF'') in random environments given by planar Scale-Invariant Random Spatial Networks ("SIRS") based on speed-marked Poisson line processes. RRF can be viewed as producing "randomly ... More
Spectral rigidity of random Schrödinger operators via Feynman-Kac formulasAug 22 2019We develop a technique for proving number rigidity (in the sense of Ghosh-Peres) of the spectrum of general random Schr\"odinger operators (RSOs). Our method makes use of Feynman-Kac formulas to estimate the variance of exponential linear statistics of ... More
On the Modelling of Uncertain Impulse Control for Continuous Markov ProcessesAug 22 2019The use of coordinate processes for the modelling of impulse control for {\em general}\ Markov processes typically involves the construction of a probability measure on a countable product of copies of the path space. In addition, admissibility of an ... More
Strategic arrivals to a queue with service rate uncertaintyAug 22 2019This paper studies the problem of strategic choice of arrival time to a single-server queue with opening and closing times when there is uncertainty regarding service speed. A Poisson population of customers need to arrive during a specified acceptance ... More
`Regression Anytime' with Brute-Force SVD TruncationAug 22 2019We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations, which arise, ... More
The conditional Gaussian multiplicative chaos structure underlying a critical continuum random polymer model on a diamond fractalAug 22 2019We discuss a Gaussian multiplicative chaos (GMC) structure underlying a family of random measures $\mathbf{M}_r$, indexed by $r\in\mathbb{R}$, on a space $\Gamma$ of directed pathways crossing a diamond fractal with Hausdorff dimension two. The laws of ... More
Real zeros of random cosine polynomials with palindromic blocks of coefficientsAug 22 2019It is well known that a random cosine polynomial $ V_n(x) = \sum_ {j=0} ^{n} a_j \cos (j x) , \ x \in (0,2 \pi) $, with the coefficients being independent and identically distributed (i.i.d.) real-valued standard Gaussian random variables (asymptotically) ... More
Brown Measures of Free Circular and Multiplicative Brownian Motions with Probabilistic Initial PointAug 22 2019Given a selfadjoint random variable $x_0$ and a unitary random variable $u$, different from Haar unitary, free from the free circular Brownian motion $c_t$ and the free multiplicative Brownian motion $b_t$, we use the Hamilton-Jacobi method to compute ... More
Concentration of Broadcast Models on TreesAug 21 2019An inequality of K. Marton shows that the joint distribution of a Markov chain with uniformly contracting transition kernels exhibits concentration. We prove an analogous inequality for broadcast models on finite trees. We use this inequality to develop ... More
Existence of probability measure valued jump-diffusions in generalized Wasserstein spacesAug 21 2019We study existence of probability measure valued jump-diffusions described by martingale problems. We develop a simple device that allows us to embed Wasserstein spaces and other similar spaces of probability measures into locally compact spaces where ... More
Doubly Reflected BSDEs in the predictable settingAug 21 2019In this paper, we introduce a specific kind of doubly reflected Backward Stochastic Differential Equations (in short DRBSDEs), defined on probability spaces equipped with general filtration that is essentially non quasi-left continuous, where the barriers ... More
A central limit theorem for the two-sided descent statistic on Coxeter groupsAug 21 2019We study the asymptotic behaviour of the statistic (des+ides) which assigns to an element w of a finite Coxeter group W the number of descents of w plus the number of descents of its inverse. Our main result is a central limit theorem for the probability ... More
Free self-decomposability and unimodality of the Fuss-Catalan distributionsAug 21 2019We study properties of the Fuss-Catalan distributions $\mu(p,r)$, $p\geq1$, $0<r\leq p$: free infinite divisibility, free self-decomposability, free regularity and unimodality. We show that the Fuss-Catalan distribution $\mu(p,r)$ is freely self-decomposable ... More
Functional CLT for the range of stable random walksAug 21 2019In this note, we establish a functional central limit theorem for the capacity of the range for a class of $\alpha$-stable random walks on the integer lattice $\mathbb{Z}^d$ with $d \ge 3\alpha$. Using similar methods, we also prove an analogous result ... More
Derivation of coupled KPZ-Burgers equation from multi-species zero-range processesAug 21 2019We consider the fluctuation fields of multi-species weakly-asymmetric zero-range interacting particle systems in one dimension, where the mass density of each species is conserved. Although such fields have been studied in systems with a single species, ... More
On conditioning a self-similar growth-fragmentation by its intrinsic areaAug 21 2019The genealogical structure of self-similar growth-fragmentations can be described in terms of a branching random walk. The so-called intrinsic area $\mathrm{A}$ arises in this setting as the terminal value of a remarkable additive martingale. Motivated ... More
Asymptotic analysis of card guessing with feedbackAug 21 2019This paper studies the game of guessing shuffled cards with feedback. A deck of $n$ cards labelled 1 to $n$ is shuffled in some fashion and placed on a table. A player tries to guess the cards from top and is given certain feedback after each guess. The ... More
Heat kernel estimates for general symmetric pure jump Dirichlet formsAug 21 2019In this paper, we consider the following symmetric non-local Dirichlet forms of pure jump type on metric measure space $(M,d,\mu)$: $$\mathcal{E}(f,g)=\int_{M\times M} (f(x)-f(y))(g(x)-g(y))\,J(dx,dy),$$ where $J(dx,dy)$ is a symmetric Radon measure on ... More
Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet formsAug 20 2019In this paper, we consider the following symmetric Dirichlet forms on a metric measure space $(M,d,\mu)$: $$\mathcal{E}(f,g) = \mathcal{E}(^{(c)}(f,g)+\int_{M\times M} (f(x)-f(y))(g(x)-g(y))\,J(dx,dy),$$ where $\mathcal{E}(^{(c)}$ is a strongly local ... More
Optimal Investment with Correlated Stochastic Volatility FactorsAug 20 2019The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a terminal time ... More
Tree Builder Random Walk: recurrence, transience and ballisticityAug 20 2019The Tree Builder Random Walk is a special random walk that evolves on trees whose size increases with time, randomly and depending upon the walker. After every s steps of the walker, a random number of vertices are added to the tree and attached to the ... More
$Λ$-linked coupling for drifting Brownian motionsAug 20 2019We raise a question on whether a dynamical system driven by Markov process is Markovian, for which we are able to propose a criterion and examples of positive case. This investigation leads us to develop (i) a general construction of intertwining dual ... More
Critical Fluctuations for the Spherical Sherrington-Kirkpatrick Model in an External FieldAug 20 2019We prove the existence of a critical regime of fluctuation of the ground-state energy of the spherical Sherrington-Kirkpatrick model in an external field. Such regime was conjectured in [2,12], and occurs with external field strength $h=O(N^{-1/6})$. ... More
Law of large numbers for the spectral radius of random matrix productsAug 20 2019We prove that the spectral radius of an i.i.d.\ random walk on $\GL_d(\C)$ satisfies a strong law of large numbers under finite second moment assumption and a weak law of large numbers under finite first moment. No irreducibility assumption is supposed. ... More
Law of large numbers for the spectral radius of random matrix productsAug 20 2019Aug 22 2019We prove that the spectral radius of an i.i.d.\ random walk on $\GL_d(\C)$ satisfies a strong law of large numbers under finite second moment assumption and a weak law of large numbers under finite first moment. No irreducibility assumption is supposed. ... More
Alignment percolationAug 20 2019The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d \ge 2$ dimensions. Salient features of the phase diagram are established in each case. The models are based on site percolation on ${\mathbb ... More
Some remarks on the direct calculation of Probabilities in Urn SchemesAug 20 2019The paper considers urn schemes in which several urns can be involved. Simplified formulas are proposed that allow direct calculation of probabilities without the use of elements combinatorics.
Multiple backward Schramm--Loewner evolution and coupling with Gaussian free fieldAug 20 2019It is known that a backward Schramm--Loewner evolution (SLE) is coupled with a free boundary Gaussian free field (GFF) with boundary perturbation to give a conformal welding of a quantum surface. Motivated by a generalization of conformal welding for ... More
Optimal Multiple Stopping Problem under Nonlinear ExpectationAug 20 2019In this paper, we study the optimal multiple stopping problem under the filtration consistent nonlinear expectations. The reward is given by a set of random variables satisfying some appropriate assumptions rather than an RCLL process. We first construct ... More
Extended Backward Stochastic Volterra Integral Equations, Quasilinear Parabolic Equations, and Feynman-Kac FormulaAug 20 2019In this paper, we establish the relationship between backward stochastic Volterra integral equations (BSVIEs, for short) and a kind of non-local quasilinear (and possibly degenerate) parabolic equations. We first introduce the extended backward stochastic ... More
Continuum models of directed polymers on disordered diamond fractals in the critical caseAug 20 2019We construct and study a family of continuum random polymer measures $\mathbf{M}_{r}$ corresponding to limiting partition function laws recently derived in a weak-coupling regime of polymer models on hierarchical graphs with marginally relevant disorder. ... More
Solution of the 15 puzzle problemAug 19 2019A generalized `$15$ puzzle' consists of an $n \times n$ numbered grid, with one missing number. A move in the game switches the position of the empty square with the position of one of its neighbors. We solve Diaconis' `15 puzzle problem' by proving that ... More
Explosion in the quasi-Gaussian HJM modelAug 19 2019We study the explosion of the solutions of the SDE in the quasi-Gaussian HJM model with a CEV-type volatility. The quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low dimensional Markovian ... More
Asymptotic degree distributions in random threshold graphsAug 19 2019We discuss several limiting degree distributions for a class of random threshold graphs in the many node regime. This analysis is carried out under a weak assumption on the distribution of the underlying fitness variable. This assumption, which is satisfied ... More
A synthetic approach to Markov kernels, conditional independence, and theorems on sufficient statisticsAug 19 2019We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning and disintegration; ... More
Taking rational numbers at randomAug 19 2019We outline some simple prescriptions to define a distribution on the set $\mathbb{Q}_0$ of all the rational numbers in $[0,1]$, and we then explore both a few properties of these distributions, and the possibility of making these rational numbers asymptotically ... More
Variance of finite difference methods for reaction networks with non-Lipschitz rate functionsAug 19 2019Parametric sensitivity analysis is a critical component in the study of mathematical models of physical systems. Due to its simplicity, finite difference methods are used extensively for this analysis in the study of stochastically modeled reaction networks. ... More
Implicit max-stable extremal integralsAug 19 2019Recently, the notion of implicit extreme value distributions has been established, which is based on a given loss function $f \ge 0$. From an application point of view, one is rather interested in extreme loss events that occur relative to $f$ than in ... More
Hunt's Hypothesis (H) for Markov Processes: Survey and BeyondAug 19 2019The goal of this paper is threefold. First, we survey the existing results on Hunt's hypothesis (H) for Markov processes and Getoor's conjecture for L\'{e}vy processes. Second, we investigate (H) for multidimensional L\'{e}vy processes from the viewpoints ... More
Bochner's Subordionation and Fractional Caloric Smoothing in Besov and Triebel--Lizorkin SpacesAug 19 2019We use Bochner's subordination technique to obtain caloric smoothing estimates in Besov- and Triebel--Lizorkin spaces. Our new estimates extend known smoothing results for the Gau{\ss}--Weierstra{\ss}, Cauchy--Poisson and higher-order generalized Gau{\ss}--Weierstra{\ss} ... More
Topological expansion in Dynkin type isomorphisms for matrix valued fieldsAug 19 2019We consider Gaussian fields of symmetric or Hermitian matrices over an electrical network, and describe how Dynkin type isomorphisms with random walks for these fields make appear topological expansions encoded by ribbon graphs. A particular case of this, ... More
On eigenvector statistics in the spherical and truncated unitary ensemblesAug 19 2019We study the overlaps between right and left eigenvectors for random matrices of the spherical and truncated unitary ensembles. Conditionally on all eigenvalues, diagonal overlaps are shown to be distributed as a product of independent random variables. ... More
A CLT for the total energy of the two-dimensional critical Ising modelAug 19 2019Consider the Ising model on $([1,2N]\times[1,2M])\cap\mathbb{Z}^2$ at critical temperature with periodic boundary condition in the horizontal direction and free boundary condition in the vertical direction. Let $E_{M,N}$ be its total energy (or Hamiltonian). ... More
Functional Limit Theorems for Marked Hawkes Point MeasuresAug 19 2019This paper establishes a functional law of large numbers and a functional central limit theorem for marked Hawkes point measures and their corresponding shot noise processes. We prove that the normalized random measure can be approximated in distribution ... More
On the rate of convergence for Takagi class functionsAug 19 2019We consider a generalized version of the Takagi function, which is one of the most famous example of nowhere differentiable continuous functions. We investigate a set of conditions to describe the rate of convergence of Takagi class functions from the ... More
A stochastic comparison result for the multitype contact process with unequal death ratesAug 19 2019A stochastic comparison result that makes progress towards understanding the classical multitype contact process with unequal death rates is given. It has long been conjectured that the particle type with the largest birth to death rate ratio survives ... More
Strong law of large numbers for a function of the local times of a transient random walk in $\mathbb Z^d$Aug 19 2019For an arbitrary transient random walk $(S_n)_{n\ge 0}$ in $\mathbb Z^d$, $d\ge 1$, we prove a strong law of large numbers for the spatial sum $\sum_{x\in\mathbb Z^d}f(l(n,x))$ of a function $f$ of the local times $l(n,x)=\sum_{i=0}^n\mathbb I\{S_i=x\}$. ... More
Beta-Binomial stick-breaking non-parametric priorAug 19 2019A new class of nonparametric prior distributions, termed Beta-Binomial stick-breaking process, is proposed. By allowing the underlying length random variables to be dependent through a Beta marginals Markov chain, an appealing discrete random probability ... More
Signature Cumulants, Ordered Partitions, and Independence of Stochastic ProcessesAug 18 2019The sequence of so-called signature moments describes the laws of many stochastic processes in analogy with how the sequence of moments describes the laws of vector-valued random variables. However, even for vector-valued random variables, the sequence ... More
Quantitative convergence rates for reversible Markov chains via strong random timesAug 18 2019Let $(X_t)$ be a discrete time Markov chain on a general state space. It is well-known that if $(X_t)$ is aperiodic and satisfies a drift and minorization condition, then it converges to its stationary distribution $\pi$ at an exponential rate. We consider ... More
The Family of Alpha,[a,b] Stochastic Orders: Risk vs. Expected ValueAug 18 2019In this paper we provide a novel family of stochastic orders, which we call the $\alpha,[a,b]$-convex decreasing and $\alpha,[a,b]$-concave increasing stochastic orders, that generalizes second order stochastic dominance. These stochastic orders allow ... More
Black-box constructions for exchangeable sequences of random multisetsAug 17 2019We develop constructions for exchangeable sequences of point processes that are rendered conditionally-i.i.d. negative binomial processes by a (possibly unknown) random measure called the base measure. Negative binomial processes are useful in Bayesian ... More
Optimal scheduling of critically loaded multiclass GI/M/n+M queues in an alternating renewal environmentAug 17 2019In this paper, we study optimal control problems for multiclass GI/M/n+M queues in an alternating renewal (up-down) random environment in the Halfin-Whitt regime. Assuming that the downtimes are asymptotically negligible and only the service processes ... More
Optimal Trapping of Brownian Motion: A Nonlinear Analogue of the Torsion FunctionAug 17 2019We study the problem of maximizing the expected lifetime of drift diffusion in a bounded domain. More formally, we consider the PDE \[ - \Delta u + b(x) \cdot \nabla u = 1 \qquad \mbox{in}~\Omega\] subject to Dirichlet boundary conditions for $\|b\|_{L^{\infty}}$ ... More
Extremal eigenvalues of sample covariance matrices with general populationAug 17 2019We analyze the behavior of the largest eigenvalues of sample covariance matrices of the form $\mathcal{Q}=(\Sigma^{1/2}X)(\Sigma^{1/2}X)^*$. The sample $X$ is an $M\times N$ rectangular random matrix with real independent entries and the population covariance ... More
Graphon-valued stochastic processes from population geneticsAug 17 2019The goal of this paper is to develop a theory of graphon-valued stochastic processes, and to construct and analyse a natural class of such processes arising from population genetics. We consider finite populations where individuals change type according ... More
Markov chains with exponential return times are finitaryAug 17 2019Consider an ergodic Markov chain on a countable state space for which the return times have exponential tails. We show that the stationary version of any such chain is a finitary factor of an i.i.d. process. A key step is to show that any stationary renewal ... More
Well-posedness and large deviations for 2-D Stochastic Navier-Stokes equations with jumpsAug 17 2019Under the classical local Lipschitz and one sided linear growth assumptions on the coefficients of the stochastic perturbations, we first prove the existence and the uniqueness of a strong (in both the probabilistic and PDEs sense) solution to the 2-D ... More
Well-posedness and large deviations for 2-D Stochastic Navier-Stokes equations with jumpsAug 17 2019Aug 20 2019Under the classical local Lipschitz and one sided linear growth assumptions on the coefficients of the stochastic perturbations, we first prove the existence and the uniqueness of a strong (in both the probabilistic and PDEs sense) solution to the 2-D ... More
On non-uniqueness in mean field gamesAug 16 2019We analyze an $N+1$-player game and the corresponding mean field game with state space $\{0,1\}$. The transition rate of $j$-th player is the sum of his control $\alpha^j$ plus a minimum jumping rate $\eta$. Instead of working under monotonicity conditions, ... More
Spatial Sobolev regularity for stochastic Burgers equations with additive trace class noiseAug 16 2019In this article we investigate the spatial Sobolev regularity of mild solutions to stochastic Burgers equations with additive trace class noise. Our findings are based on a combination of suitable bootstrap-type arguments and a detailed analysis of the ... More
Stationary Directed Polymers and Energy Solutions of the Burgers EquationAug 16 2019We consider the stationary O'Connell-Yor model of semi-discrete directed polymers in a Brownian environment in the intermediate disorder regime and show convergence of the increments of the log-partition function to the energy solutions of the stochastic ... More
A finitary structure theorem for vertex-transitive graphs of polynomial growthAug 16 2019We prove a quantitative, finitary version of Trofimov's result that a connected, locally finite vertex-transitive graph G of polynomial growth admits a quotient with finite fibres on which the action of Aut(G) is virtually nilpotent with finite vertex ... More
Weighted Lépingle inequalityAug 16 2019We prove an estimate for weighted $p$-th moments of the pathwise $r$-variation of a martingale in terms of the $A_{p}$ characteristic of the weight.
On the optimality of double barrier strategies for Lévy processesAug 16 2019This paper studies the de Finetti's optimal dividend problem with capital injection. We confirm the optimality of a double barrier strategy when the underlying risk model follows a L\'evy process which may have positive and negative jumps. The main result ... More
Brownian Loops, Layering Fields and Imaginary Gaussian Multiplicative ChaosAug 16 2019We study vertex-like operators built from the Brownian loop soup in the limit as the loop soup intensity tends to infinity. More precisely, following Camia, Gandolfi and Kleban (Nuclear Physics B 902, 2016), we take a Brownian loop soup in a planar domain ... More
Kernel Sketching yields Kernel JLAug 16 2019The main contribution of the paper is to show that Gaussian sketching of a kernel-Gram matrix $\mathbf{K}$ yields an operator whose counterpart in an RKHS $\mathcal{H}$, is a random projection operator---in the spirit of Johnson-Lindenstrauss (JL) lemma. ... More
Correlation function methods for a system of annihilating Brownian particlesAug 15 2019In this expository note we aim to highlight the correlation function method as a unified approach in proving both hydrodynamic limits and fluctuation limits. We review the key steps in establishing the functional law of large numbers for a simple stochastic ... More
Mean-field limit and numerical analysis for Ensemble Kalman Inversion: linear settingAug 15 2019Ensemble Kalman inversion (EKI) is a method introduced in [14] to find samples from the target posterior distribution in the Bayesian formulation. As a deviation from Ensemble Kalman filter [6], it introduces a pseudo-time along which the particles sampled ... More
Mean-field limit and numerical analysis for Ensemble Kalman Inversion: linear settingAug 15 2019Aug 16 2019Ensemble Kalman inversion (EKI) is a method introduced in [14] to find samples from the target posterior distribution in the Bayesian formulation. As a deviation from Ensemble Kalman filter [6], it introduces a pseudo-time along which the particles sampled ... More
Random surfaces and Liouville quantum gravityAug 15 2019Liouville quantum gravity (LQG) surfaces are a family of random fractal surfaces which can be thought of as the canonical models of random two-dimensional Riemannian manifolds, in the same sense that Brownian motion is the canonical model of a random ... More
Mean-variance hedging of unit linked life insurance contracts in a jump-diffusion modelAug 15 2019We consider a time-consistent mean-variance portfolio selection problem of an insurer and allow for the incorporation of basis (mortality) risk. The optimal solution is identified with a Nash subgame perfect equilibrium. We characterize an optimal strategy ... More
Self-Exciting Multifractional ProcessesAug 15 2019We propose a new multifractional stochastic process which allows for self-exciting behavior, similar to what can be seen for example in earthquakes and other self-organizing phenomena. The process can be seen as an extension of a multifractional Brownian ... More
Epidemic models on social networks -- with inferenceAug 15 2019Consider stochastic models for the spread of an infection in a structured community, where this structured community is itself described by a random network model. Some common network models and transmission models are defined and large population proporties ... More
On the anisotropic stable JCIR processAug 15 2019We investigate the anisotropic stable JCIR process which is a multi-dimensional extension of the stable JCIR process but also a multi-dimensional analogue of the classical JCIR process. We prove that the heat kernel of the anisotropic stable JCIR process ... More
Robust estimation of the mean with bounded relative standard deviationAug 15 2019Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples of this type ... More
Moments of the weighted Cantor measuresAug 14 2019Based on the seminal work of Hutchinson, we investigate properties of {\em $\alpha$-weighted Cantor measures} whose support is a fractal contained in the unit interval. Here, $\alpha$ is a vector of nonnegative weights summing to $1$, and the corresponding ... More
Limit Theorems for the Length of the Longest Common Subsequence of Mallows PermutationsAug 14 2019The Mallows measure is measure on permutations which was introduced by Mallows in connection with ranking problems in statistics. Under this measure, the probability of a permutation $\pi$ is proportional to $q^{Inv(\pi)}$ where $q$ is a positive parameter ... More
On discrete loop signatures and Markov loops topologyAug 14 2019Our purpose is to explore, in the context of loop ensembles on finite graphs, the relations between combinatorial group theory, loops topology, loop measures, and signatures of discrete paths. We determine the distributions of the loop homotopy class, ... More
Randomly coupled differential equations with correlationsAug 14 2019We consider the long time asymptotic behavior of a large system of $N$ linear differential equations with random coefficients. We allow for general correlation structures \nc among the coefficients, thus we substantially generalize our previous work [14] ... More
Fluctuations of propagation front in catalytic branching walkAug 14 2019We consider a supercritical catalytic branching random walk (CBRW) on a multidimensional lattice Z^d (d is positive integer). The main subject of study is the behavior of particles cloud in space and time. For CBRW on an integer line, Carmona and Hu (2014) ... More
Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic ForcingAug 13 2019We survey some recent developments in the analysis of the long-time behavior of stochastic solutions of nonlinear conservation laws driven by stochastic forcing. Moreover, we establish the existence and uniqueness of invariant measures for anisotropic ... More
Local convergence of random planar graphsAug 13 2019The present work describes the asymptotic local shape of a graph drawn uniformly at random from all connected simple planar graphs with n labelled vertices. We establish a novel uniform infinite planar graph (UIPG) as quenched limit in the local topology ... More
Rerooting multi-type branching trees: the infinite spine caseAug 13 2019We prove local convergence results of rerooted conditioned multi-type Galton-Watson trees. The limit objects are multitype variants of the random sin-tree constructed by Aldous (1991), and differ according to which types recur infinitely often along the ... More
On Occupancy Moments and Bloom Filter EfficiencyAug 13 2019Two multivariate committee distributions are shown to belong to Berg's family of factorial series distributions and Kemp's family of generalized hypergeometric factorial moment distributions. Exact moment formulas, upper and lower bounds, and statistical ... More
$p$-adic Integral GeometryAug 13 2019We prove a $p$-adic version of the Integral Geometry Formula for averaging the intersection of two $p$-adic projective algebraic sets. We apply this result to give bounds on the number of points in the modulo $p^m$ reduction of a projective set (reproving ... More
On explicit $L^2$-convergence rate estimate for underdamped Langevin dynamicsAug 13 2019We provide a new explicit estimate of exponential decay rate of underdamped Langevin dynamics in $L^2$ distance. To achieve this, we first prove a Poincar\'{e}-type inequality with Gibbs measure in space and Gaussian measure in momentum. Our new estimate ... More
Some harmonic functions for killed Markov branching processes with immigration and cullingAug 13 2019For a continuous-time Bienaym\'e-Galton-Watson process, $X$, with immigration and culling, $0$ as an absorbing state, call $X^q$ the process that results from killing $X$ at rate $q\in (0,\infty)$, followed by stopping it on extinction or explosion. Then ... More
Time-changed Dirac-Fokker-Planck equations on the latticeAug 13 2019A time-changed discretization for the Dirac equation is proposed. More precisely, we consider a Dirac equation with discrete space and continuous time perturbed by a time-dependent diffusion term $\sigma^2Ht^{2H-1}$ that resembles to a latticizing version ... More
Integration by parts formula for killed processes: A point of view from approximation theoryAug 13 2019In this paper, we establish a probabilistic representation for two integration by parts formulas, one being of Bismut-Elworthy-Li's type, for the marginal law of a one-dimensional diffusion process killed at a given level. These formulas are established ... More
Growth of Common Friends in a Preferential Attachment ModelAug 13 2019The number of common friends (or connections) in a graph is a commonly used measure of proximity between two nodes. Such measures are used in link prediction algorithms and recommendation systems in large online social networks. We obtain the rate of ... More
On breadth-first constructions of scaling limits of random graphs and random unicellular mapsAug 12 2019We give alternate constructions of (i) the scaling limit of the uniform connected graphs with given fixed surplus, and (ii) the continuum random unicellular map (CRUM) of a given genus that start with a suitably tilted Brownian continuum random tree and ... More
Collective marks and first passage timesAug 12 2019Probability generating functions for first passage times of Markov chains are found using the method of collective marks. A system of equations is found which can be used to obtain moments of the first passage times.
Percolation phase transitions for the SIR model with random powersAug 12 2019This thesis considers three models which describe a multihop ad-hoc telecommunication system. These systems consist of users sending messages, which can jump to other users to reach the target user. The first two models have already been examined extensively, ... More
The quasi-stationary distribution of the subcritical contact processAug 12 2019We show that the quasi-stationary distribution of the subcritical contact process on $\mathbb{Z}^d$ is unique. This is in contrast with other processes which also do not come down from infinity, like stable queues and Galton-Watson, and it seems to be ... More
Asymptotic properties of permanental sequencesAug 12 2019Let $U=\{U_{j,k},j,k\in \overline {\mathbb N}\}$ be the potential of a transient symmetric Borel right process $X$ with state space $\overline {\mathbb N}$. For any excessive function $f=\{f_{k,k\in \overline {\mathbb N}}\}$ for $X$ , $\widetilde U=\{\widetilde ... More
High-frequency analysis of parabolic stochastic PDEs with multiplicative noise: Part IAug 12 2019We consider the stochastic heat equation driven by a multiplicative Gaussian noise that is white in time and spatially homogeneous in space. Assuming that the spatial correlation function is given by a Riesz kernel of order $\alpha \in (0,1)$, we prove ... More
Living on the edge of instabilityAug 12 2019Statistical description of stochastic dynamics in highly unstable potentials is strongly affected by properties of divergent trajectories, that quickly leave meta-stable regions of the potential landscape and never return. Using ideas from theory of Q-processes ... More
Matrix-analytic solution of system of integral equations in three tandem serversAug 12 2019A matrix-analytic method is proposed for solving a system of linear integral equations arises in three tandem servers. The approach is by modelling the cumulative distribution function (cdf) of the service time as a matrix exponential function. The method ... More