Latest in math.pr

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On bulk deviations for the local behavior of random interlacementsJun 13 2019We investigate certain large deviation asymptotics concerning random interlacements in Z^d, d bigger or equal to 3. We find the principal exponential rate of decay for the probability that the average value of some suitable non-decreasing local function ... More
Microscopic and macroscopic perspectives on stationary nonequilibrium statesJun 13 2019The main subject of the thesis is the study of stationary nonequilibrium states trough the use of microscopic stochastic models that encode the physical interaction in the rules of Markovian dynamics for particles configurations. These models are known ... More
The rank of sparse random matricesJun 13 2019Generalising prior work on the rank of random matrices over finite fields [Coja-Oghlan and Gao 2018], we determine the rank of a random matrix with prescribed numbers of non-zero entries in each row and column over any field. The rank formula turns out ... More
Anderson localisation in stationary ensembles of quasiperiodic operatorsJun 13 2019An ensemble of quasi-periodic discrete Schr\"{o}dinger operators with an arbitrary number of basic frequencies is considered, in a lattice of arbitrary dimension, in which the hull function is a realisation of a stationary Gaussian process on the torus. ... More
Quasi-Stationary Distributions and Resilience: What to get from a sample?Jun 13 2019We study a class of multi-species birth-and-death processes going almost surely to extinction and admitting a unique quasi-stationary distribution (qsd for short). When rescaled by $K$ and in the limit $K\to+\infty$, the realizations of such processes ... More
Strategic customer behavior in a queueing system with alternating information structureJun 13 2019Strategic customer behavior is strongly influenced by the level of information that is provided to customers. Hence, to optimize the design of queueing systems, many studies consider various versions of the same service model and compare them under different ... More
Densities for piecewise deterministic Markov processes with boundaryJun 13 2019We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In our approach ... More
Localization in Gaussian disordered systems at low temperatureJun 13 2019For a broad class of Gaussian disordered systems at low temperature, we show that the Gibbs measure is asymptotically localized in small neighborhoods of a small number of states. From a single argument, we obtain (i) a version of "complete" path localization ... More
Conditional Monte Carlo for Reaction NetworksJun 12 2019Reaction networks are often used to model interacting species in fields such as biochemistry and ecology. When the counts of the species are sufficiently large, the dynamics of their concentrations are typically modeled via a system of differential equations. ... More
Equality and difference of quenched and averaged large deviation rate functions for random walks in random environments without ballisticityJun 12 2019Consider a multidimensional random walk in a uniformly elliptic random environment. Varadhan (\cite{V03}) showed that the rescaled location of the random walks satisfies both an almost sure (quenched) as well as an averaged (annealed) large deviation ... More
Matrix Mittag--Leffler distributions and modeling heavy-tailed risksJun 12 2019In this paper we define the class of matrix Mittag-Leffler distributions and study some of its properties. We show that it can be interpreted as a particular case of an inhomogeneous phase-type distribution with random scaling factor. We then identify ... More
Asymptotic approach for backward stochastic differential equation with singular terminal condition *Jun 12 2019In this paper, we provide a one-to-one correspondence between the solution Y of a BSDE with singular terminal condition and the solution H of a BSDE with singular generator. This result provides the precise asymptotic behavior of Y close to the final ... More
A second order analysis of McKean-Vlasov semigroupsJun 12 2019We propose a second order differential calculus to analyze the regularity and the stability properties of the distribution semigroup associated with McKean-Vlasov diffusions. This methodology provides second order Taylor type expansions with remainder ... More
Biased random k-SATJun 12 2019The basic random $k$-SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables, is the conjunction of these clauses satisfiable? Here we consider a variation ... More
De Finetti's control problem with Parisian ruin for spectrally negative Lévy processesJun 12 2019We consider de Finetti's stochastic control problem when the (controlled) process is allowed to spend time under the critical level. More precisely, we consider a generalized version of this control problem in a spectrally negative L\'evy model with exponential ... More
Activated Random Walks on $\mathbb{Z}^d$Jun 12 2019Some stochastic systems are particularly interesting as they exhibit critical behavior without fine-tuning of a parameter, a phenomenon called self-organized criticality. In the context of driven-dissipative steady states, one of the main models is that ... More
Convergence of partial sum processes to stable processes with application for aggregation of branching processesJun 12 2019We provide a generalization of Theorem 1 in Bartkiewicz, Jakubowski, Mikosch and Wintenberger (2011) in the sense that we give sufficient conditions for weak convergence of finite dimensional distributions of the partial sum processes of a strongly stationary ... More
Polynomially growing harmonic functions on connected groupsJun 12 2019We study the connection between the dimension of certain spaces of harmonic functions on a group and its geometric and algebraic properties. Our main result shows that (for sufficiently "nice" random walk measures) a connected, compactly generated, locally ... More
Gambler's ruin estimates on finite inner uniform domainsJun 12 2019Gambler's ruin estimates can be viewed as harmonic measure estimates for finite Markov chains which are absorbed (or killed) at boundary points. We relate such estimates to properties of the underlying chain and its Doob transform. Precisely, we show ... More
Analytic-geometric methods for finite Markov chains with applications to quasi-stationarityJun 12 2019For a relatively large class of well-behaved absorbing (or killed) finite Markov chains, we give detailed quantitative estimates regarding the behavior of the chain before it is absorbed (or killed). Typical examples are random walks on box-like finite ... More
Homological Connectivity in Random Čech ComplexesJun 11 2019Jun 13 2019We study the homology of random \v{C}ech complexes generated by a homogeneous Poisson process. We focus on 'homological connectivity' - the stage where the random complex is dense enough, so that its homology "stabilizes" and becomes isomorphic to that ... More
Homological Connectivity in Čech ComplexesJun 11 2019We study the homology of random \v{C}ech complexes generated by a homogeneous Poisson process. We focus on 'homological connectivity' - the stage where the random complex is dense enough, so that its homology "stabilizes" and becomes isomorphic to that ... More
Modified log-Sobolev inequality for a compact PJMP with degenerate jumpsJun 11 2019We study the modified log-Sobolev inequality for a class of pure jump Markov processes that describe the interactions between brain neurons. In particular, we focus on a finite and compact process with degenerate jumps inspired by the model introduced ... More
Path Cohomology of Locally Finite Digraphs,Hodge's Theorem and the $p$-Lazy Random WalkJun 11 2019In this paper we generalize the path cohomology of digraphs to a locally finite digraph $G=(V,E)$. We prove a Hodge Decomposition Theorem and show some relations with the $p$-lazy Random Walk.
Asymptotic analysis of exit time for dynamical systems with a single well potentialJun 11 2019We study the exit time from a bounded multi-dimensional domain $\Omega$ of the stochastic process $\mathbf{Y}_\varepsilon=\mathbf{Y}_\varepsilon(t,a)$, $t\geqslant 0$, $a\in \mathcal{A}$, governed by the overdamped Langevin dynamics \begin{equation*} ... More
A proof of the mean-field limit for $λ$-convex potentials by $Γ$-ConvergenceJun 11 2019In this work we give a proof of the mean-field limit for $\lambda$-convex potentials using a purely variational viewpoint. Our approach is based on the observation that all evolution equations that we study can be written as gradient flows of functionals ... More
Elephant random walks with delaysJun 11 2019In the simple random walk the steps are independent, viz., the walker has no memory. In contrast, in the Elephant Random walk (ERW), which was introduced by Sch\"utz and Trimper in 2004, the walker remembers the whole past, and the next step always depends ... More
Upper envelopes of families of Feller semigroups and viscosity solutions to a class of nonlinear Cauchy problemsJun 11 2019In this paper we construct the smallest semigroup $\mathscr{S}$ that dominates a given family of linear Feller semigroups. The semigroup $\mathscr{S}$ will be referred to as the semigroup envelope or Nisio semigroup. In a second step we investigate strong ... More
Schwinger-Dyson and loop equations for a product of square Ginibre random matricesJun 11 2019In this paper, we study the product of two complex Ginibre matrices and the loop equations satisfied by their resolvents (i.e. the Stieltjes transform of the correlation functions). We obtain using Schwinger-Dyson equation (SDE) techniques the general ... More
Anderson-Bernoulli Localization on the 3D lattice and discrete unique continuation principleJun 11 2019We consider the Anderson model with Bernoulli potential on $\mathbb{Z}^{3}$, and prove localization of eigenfunctions corresponding to eigenvalues near zero, the lower boundary of the spectrum. The proof follows the framework by Bourgain--Kenig and Ding--Smart. ... More
The shape of shortest paths in random spatial networksJun 10 2019In the classic model of first passage percolation, for pairs of vertices separated by a Euclidean distance $L$, geodesics exhibit deviations from their mean length $L$ that are of order $L^\chi$, while the transversal fluctuations, known as wandering, ... More
On Mean Field Limit and Quantitative Estimates with a Large Class of Singular Kernels: Application to the Patlak-Keller-Segel ModelJun 10 2019In this note, we propose a new relative entropy combination of the methods developed by P.--E. Jabin and Z.~Wang [Inventiones (2018)] and by S. Serfaty [Proc. Int. Cong. of Math, (2018) and references therein] to treat more general kernels in mean field ... More
Stochastic PDE limit of the dynamic ASEPJun 10 2019We study a stochastic PDE limit of the height function of the dynamic asymmetric simple exclusion process (dynamic ASEP). A degeneration of the stochastic Interaction Round-a-Face (IRF) model of arXiv:1701.05239, dynamic ASEP has a jump parameter $q\in ... More
Coalescence for a Galton-Watson process with immigrationJun 10 2019In this paper, we consider a Galton-Watson process with immigration. Pick $i(\ge2)$ individuals randomly without replacement from the $n$-th generation and trace their lines of descent back in time till they coalesce into $1$ individual in a certain generation, ... More
Propagation of chaos for a General Balls into Bins dynamicsJun 10 2019Consider $N$ balls initially placed in $L$ bins. At each time step take a ball from each non-empty bin and \emph{randomly} reassign the balls into the bins.We call this finite Markov chain \emph{General Repeated Balls into Bins} process. It is a discrete ... More
Loop-erased partitioning of a graphJun 10 2019We consider a random partition of the vertex set of an arbitrary graph that can be efficiently sampled using loop-erased random walks stopped at a random independent exponential time of parameter $q>0$. The related random blocks tend to cluster nodes ... More
On the Optimality of Sparse Model-Based Planning for Markov Decision ProcessesJun 10 2019This work considers the sample complexity of obtaining an $\epsilon$-optimal policy in a discounted Markov Decision Process (MDP), given only access to a generative model. In this model, the learner accesses the underlying transition model via a sampling ... More
The Impact of Regularization on High-dimensional Logistic RegressionJun 10 2019Jun 12 2019Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic regression are ... More
The Impact of Regularization on High-dimensional Logistic RegressionJun 10 2019Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic regression are ... More
Norms of weighted sums of log-concave random vectorsJun 09 2019Let $C$ and $K$ be centrally symmetric convex bodies of volume $1$ in ${\mathbb R}^n$. We provide upper bounds for the multi-integral expression \begin{equation*}\|{\bf t}\|_{C^s,K}=\int_{C}\cdots\int_{C}\Big\|\sum_{j=1}^st_jx_j\Big\|_K\,dx_1\cdots dx_s\end{equation*} ... More
A note on norms of signed sums of vectorsJun 09 2019Our starting point is an improved version of a result of D. Hajela related to a question of Koml\'{o}s: we show that if $f(n)$ is a function such that $\lim\limits_{n\to\infty }f(n)=\infty $ and $f(n)=o(n)$, there exists $n_0=n_0(f)$ such that for every ... More
Finitary Boolean functionsJun 09 2019We study functions on the infinite-dimensional Hamming cube $\{-1,1\}^\infty$, in particular Boolean functions into $\{-1,1\}$, generalising results on analysis of Boolean functions on $\{-1,1\}^n$ for $n\in\mathbb{N}$. The notion of noise sensitivity, ... More
Prokhorov-like conditions for weak compactness of sets of bounded Radon measures on different topological spacesJun 09 2019The paper presents some weak compactness criterion for a subset $M$ of the set $\mathfrak{RM}_b(T,\mathcal{G})$ of all positive bounded Radon measures on a Hausdorff topological space $(T,\mathcal{G})$ similar to the Prokhorov criterion for a complete ... More
High-dimensional limit theorems for random vectors in $\ell_p^n$-balls. IIJun 09 2019In this article we prove three fundamental types of limit theorems for the $q$-norm of random vectors chosen at random in an $\ell_p^n$-ball in high dimensions. We obtain a central limit theorem, a moderate deviations as well as a large deviations principle ... More
Linear Dimension Reduction Approximately Preserving a Function of the 1-NormJun 08 2019For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are not too close, ... More
A Note on the Mean Residual Life Function of the Cantor DistributionJun 08 2019In this note, we consider the mean residual life (MRL) function of the Cantor distribution and study its properties. We show that the MRL function is continuous at all points, locally decreasing at all points outside the Cantor set and has a unique fixed ... More
Convergence in Density of Splitting AVF Scheme for Stochastic Langevin EquationJun 08 2019In this article, we study the density function of the numerical solution of the splitting averaged vector field (AVF) scheme for the stochastic Langevin equation. To deal with the non-globally monotone coefficient in the considered equation, we first ... More
Asymptotic Formulas for Empirical Measures of (Reflecting) Diffusion Processes on Riemannian ManifoldsJun 08 2019Let $M$ be a compact connected Riemannian manifold possibly with a boundary, let $V\in C^2(M)$ such that $\mu(d x):=e^{V(x)}d x$ is a probability measure, and let $\{\lambda_i\}_{i\ge 1} $ be all non-trivial eigenvalues of $-L$ with Neumann boundary condition ... More
Lifschitz tail for alloy-type models driven by the fractional LaplacianJun 08 2019We establish precise asymptotics near zero of the integrated density of states for the random Schr\"{o}dinger operators $(-\Delta)^{\alpha/2} + V^{\omega}$ in $L^2(\mathbb R^d)$ for the full range of $\alpha\in(0,2]$ and a fairly large class of random ... More
Asymptotically Optimal Change Point Detection for Composite Hypothesis in State Space ModelsJun 08 2019This paper investigates change point detection in state space models, in which the pre-change distribution $f^{\theta_0}$ is given, while the poster distribution $f^{\theta}$ after change is unknown. The problem is to raise an alarm as soon as possible ... More
An optimal transport problem with backward martingale constraints motivated by insider tradingJun 07 2019We study a single-period optimal transport problem on $\mathbb{R}^2$ with a covariance-type cost function $c(x,y) = (x_1-y_1)(x_2-y_2)$ and a backward martingale constraint. We show that a transport plan $\gamma$ is optimal if and only if there is a maximal ... More
Sunklodas' approach to normal approximation for time-dependent dynamical systemsJun 07 2019We consider time-dependent dynamical systems arising as sequential compositions of self-maps of a probability space. We establish conditions under which the Birkhoff sums for multivarate observations, given a centering and a general normalizing sequence ... More
Finite Markov chains coupled to general Markov processes and an application to metastabilityJun 07 2019We consider a diffusion given by a small noise perturbation of a dynamical system driven by a potential function with a finite number of local minima. The classical results of Freidlin and Wentzell show that the time this diffusion spends in the domain ... More
Hypercontractivity, and Lower Deviation Estimates in Normed SpacesJun 07 2019We consider the problem of estimating probabilities of lower deviation $\mathbb P\{\|G\| \leqslant \delta \mathbb E\|G\|\}$ in normed spaces with respect to the Gaussian measure. These estimates occupy central role in the probabilistic study of high-dimensional ... More
Random walk on the simple symmetric exclusion processJun 07 2019We investigate the long-term behavior of a random walker evolving on top of the simple symmetric exclusion process (SSEP) at equilibrium, in dimension one. At each jump, the random walker is subject to a drift that depends on whether it is sitting on ... More
A comparison principle between rough and non-rough Heston models - with applications to the volatility surfaceJun 07 2019We present a number of related comparison results, which allow to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on a comparison ... More
Limit theory for unbiased and consistent estimators of statistics of random tessellationsJun 07 2019We observe a realization of a stationary generalized weighted Voronoi tessellation of the d-dimensional Euclidean space within a bounded observation window. Given a geometric characteristic of the typical cell, we use the minus-sampling technique to construct ... More
A Central Limit Theorem for the number of descents and some urn modelsJun 07 2019The purpose of this work is to establish a central limit theorem that can be applied to a particular form of Markov chains, including the number of descents in a random permutation of $\mathfrak{S}_n$, two-type generalized P\'olya urns, and some other ... More
Approximation of exit times for one-dimensional linear and growth diffusion processesJun 07 2019In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and in the Ornstein-Uhlenbeck context. Here the aim is ... More
A ruin model with a resampled environmentJun 07 2019This paper considers a Cram\'er-Lundberg risk setting, where the components of the underlying model change over time. These components could be thought of as the claim arrival rate, the claim-size distribution, and the premium rate, but we allow the more ... More
Limits on amplifiers of natural selection under death-Birth updatingJun 06 2019The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation probability of advantageous ... More
The correlation function of a queue with Levy and Markov additive inputJun 06 2019Let $(Q_t)$ be a stationary workload process, and $r(t)$ the correlation coefficient of $Q_0$ and $Q_t$. In a series of previous papers (i) the transform of $r(\cdot)$ has been derived for the case that the driving process is spectrally-positive (sp) ... More
A Class of Random Recursive Tree Algorithms with DeletionJun 06 2019We examine a discrete random recursive tree growth process that, at each time step, either adds or deletes a node from the tree with probability $p$ and $1-p$, respectively. Node addition follows the usual uniform attachment model. For node removal, we ... More
The Contextuality-by-Default View of the Sheaf-Theoretic Approach to ContextualityJun 06 2019The Sheaf-Theoretic Contextuality (STC) theory developed by Abramsky and colleagues is a very general account of whether multiply overlapping subsets of a set, each of which is endowed with certain "local'" structure, can be viewed as inheriting this ... More
A dual process for the coupled Wright-Fisher diffusionJun 06 2019The coupled Wright-Fisher diffusion is a multi-dimensional Wright-Fisher diffusion for multi-locus and multi-allelic genetic frequencies, expressed as the strong solution to a system of stochastic differential equations that are coupled in the drift, ... More
Bargmann-Fock percolation is noise sensitiveJun 06 2019We show that planar Bargmann-Fock percolation is noise sensitive under the Ornstein-Ulhenbeck process. The proof is based on the randomized algorithm approach introduced by Schramm and Steif and gives quantitative polynomial bounds on the noise sensitivity ... More
Exponential integrability and exit times of diffusions on sub-Riemannian and RCD*(K,N) spacesJun 06 2019In this article we derive moment estimates, exponential integrability, concentration inequalities and exit times estimates for canonical diffusions in two settings each beyond the scope of Riemannian geometry. Firstly, we consider sub-Riemannian limits ... More
Assouad spectrum thresholds for some random constructionsJun 06 2019The Assouad dimension of a metric space determines its extremal scaling properties. The derived notion of the Assouad spectrum fixes relative scales by a scaling function to obtain interpolation behaviour between the quasi-Assouad and box-counting dimensions. ... More
Criticality of measures on 2-d Ising configurations: from square to hexagonal graphsJun 06 2019On the space of Ising configurations on the 2-d square lattice, we consider a family of non Gibbsian measures introduced by using a pair Hamiltonian, depending on an additional inertial parameter $q$. These measures are related to the usual Gibbs measure ... More
A note on eigenvalues estimates for one-dimensional diffusion operatorsJun 06 2019Dealing with one-dimensional diffusion operators, we obtain upper and lower variational formulae on the eigenvalues given by the max-min principle, generalizing the celebrated result of Chen and Wang on the spectral gap. Our inequalities reveal to be ... More
Asymptotic normality for random simplices and convex bodies in high dimensionsJun 06 2019Central limit theorems for the log-volume of a class of random convex bodies in $\mathbb{R}^n$ are obtained in the high-dimensional regime, that is, as $n\to\infty$. In particular, the case of random simplices pinned at the origin and simplices where ... More
All Terminal Reliability Roots of Smallest ModulusJun 05 2019Given a connected graph $G$ whose vertices are perfectly reliable and whose edges each fail independently with probability $q\in[0,1],$ the \textit{(all-terminal) reliability} of $G$ is the probability that the resulting subgraph of operational edges ... More
Quasi-invariance of fractional Gaussian fields nonlinear wave equation with polynomial nonlinearityJun 05 2019We prove quasi-invariance of Gaussian measures $\mu_s$ with Cameron-Martin space $H^s$ under the flow of the defocusing nonlinear wave equation with polynomial nonlinearities of any order for all $s>5/2$, including fractional $s$. This extends work of ... More
Typical dynamics and fluctuation analysis of slow-fast systems driven by fractional Brownian motionJun 05 2019This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we characterize ... More
Infinite paths on a random environment of $\mathbb{Z}^2$ with bounded and recurrent sumsJun 05 2019This paper considers a random structure on the lattice $\mathbb{Z}^2$ of the following kind. To each edge $e$ a random variable $X_e$ is assigned, together with a random sign $Y_e \in \{-1,+1\}$. For an infinite self-avoiding path on $\mathbb{Z}^2$ starting ... More
Renewal Time Points for Hawkes ProcessesJun 05 2019In the last decade Hawkes processes have received much attention as models for functional connectivity in neural spiking networks and other dynamical systems with a cascade behavior. In this paper we establish a renewal approach for analyzing this process. ... More
Impact of Prior Knowledge and Data Correlation on Privacy Leakage: A Unified AnalysisJun 05 2019It has been widely understood that differential privacy (DP) can guarantee rigorous privacy against adversaries with arbitrary prior knowledge. However, recent studies demonstrate that this may not be true for correlated data, and indicate that three ... More
Foundations of Constructive Probability TheoryJun 05 2019We provide a systematic, thorough treatment of the foundations of probability theory and stochastic processes along the lines of E. Bishop's constructive analysis. Every existence result presented shall be a construction; and the input data, the construction ... More
The simple exclusion process on finite connected graphsJun 04 2019Consider a system of $K$ particles moving on the vertex set of a finite connected graph with at most one particle per vertex. If there is one, the particle at $x$ chooses one of the $\hbox{deg} (x)$ neighbors of its location uniformly at random at rate ... More
Optimal auction duration: A price formation viewpointJun 04 2019We consider an auction market in which market makers fill the order book during a given time period while some other investors send market orders. We define the clearing price of the auction as the price maximizing the exchanged volume at the clearing ... More
Solution of the Kolmogorov equation for TASEPJun 04 2019We provide a direct and elementary proof that the formula obtained in [MQR17] for the TASEP transition probabilities for general (one-sided) initial data solves the Kolmogorov backward equation. The same method yields the solution for the related PushASEP ... More
Counting independent sets in unbalanced bipartite graphsJun 04 2019We give an FPTAS for approximating the partition function of the hard-core model for bipartite graphs when there is sufficient imbalance in the degrees or fugacities between the sides $(L,R)$ of the bipartition. This includes, among others, the biregular ... More
The Dirichlet problem for orthodiagonal mapsJun 04 2019We prove that the discrete harmonic function corresponding to smooth Dirichlet boundary conditions on orthodiagonal maps, that is, plane graphs having quadrilateral faces with orthogonal diagonals, converges to its continuous counterpart as the mesh size ... More
A combinatorial criterion for macroscopic circles in planar triangulationsJun 04 2019Given a finite simple triangulation, we estimate the sizes of circles in its circle packing in terms of Cannon's vertex extremal length. Our estimates provide control over the size of the largest circle in the packing. We use them, combined with results ... More
How much can the eigenvalues of a random Hermitian matrix fluctuate?Jun 04 2019The goal of this article is to study how much the eigenvalues of large Hermitian random matrices deviate from certain deterministic locations -- or in other words, to investigate optimal rigidity estimates for the eigenvalues. We do this in the setting ... More
Successive minimum spanning treesJun 04 2019In a complete graph $K_n$ with edge weights drawn independently from a uniform distribution $U(0,1)$ (or alternatively an exponential distribution $\operatorname{Exp}(1)$), let $T_1$ be the MST (the spanning tree of minimum weight) and let $T_k$ be the ... More
Scenario approach for minmax optimization with emphasis on the nonconvex case: positive results and caveatsJun 04 2019Jun 05 2019We treat the so-called scenario approach, a popular probabilistic approximation method for robust minmax optimization problems via independent and indentically distributed (i.i.d) sampling from the uncertainty set, from various perspectives. The scenario ... More
Extinction time of logistic branching processes in a Brownian environmentJun 04 2019In this paper, we study the extinction time of logistic branching processes which are perturbed by an independent random environment driven by a Brownian motion. Our arguments use a Lamperti-type representation which is interesting on its own right and ... More
Exit problem for Ornstein-Uhlenbeck processes: a random walk approachJun 04 2019In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm so-called Walk on Moving Spheres was already introduced in the Brownian context. The aim is therefore to generalize ... More
On Expansions and Nodes for Sparse Grid Collocation of Lognormal Elliptic PDEsJun 04 2019This work is a follow-up on a previous contribution (`Convergence of sparse collocation for functions of countably many Gaussian random variables (with application to elliptic PDEs)' SIAM Journal of Numerical Analysis 2018), and contains further insights ... More
A control variate method driven by diffusion approximationJun 04 2019In this paper we examine a control variate estimator for a quantity that can be expressed as the expectation of a functional of a random process, that is itself the solution of a differential equation driven by fast mean-reverting ergodic forces. The ... More
Snackjack: A toy model of blackjackJun 04 2019Snackjack is a highly simplified version of blackjack that was proposed by Ethier (2010) and given its name by Epstein (2013). The eight-card deck comprises two aces, two deuces, and four treys, with aces having value either 1 or 4, and deuces and treys ... More
The asymptotic error of chaos expansion approximations for stochastic differential equationsJun 04 2019In this paper we present a numerical scheme for stochastic differential equations based upon the Wiener chaos expansion. The approximation of a square integrable stochastic differential equation is obtained by cutting off the infinite chaos expansion ... More
Martingale Representation in the Enlargement of the Filtration Generated by a Point ProcessJun 04 2019Let $X$ be a point process and let $\mathbb{X}$ denote the filtration generated by $X$. In this paper we study the martingale representation in the filtration $\mathbb{G}$ obtained as an initial and progressive enlargement of the filtration $\mathbb{X}$. ... More
Multi-time distribution in discrete polynuclear growthJun 03 2019We study the multi-time distribution in a discrete polynuclear growth model or, equivalently, in directed last-passage percolation with geometric weights. A formula for the joint multi-time distribution function is derived in the discrete setting. It ... More
Quantitative Propagation of Chaos in the bimolecular chemical reaction-diffusion modelJun 03 2019We study a stochastic system of $N$ interacting particles which models bimolecular chemical reaction-diffusion. In this model, each particle $i$ carries two attributes: the spatial location $X_t^i\in \mathbb{T}^d$, and the type $\Xi_t^i\in \{1,\cdots,n\}$. ... More
Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphsJun 03 2019The spatial structure of an evolving population affects which mutations become fixed. Some structures amplify selection, increasing the likelihood that beneficial mutations become fixed while deleterious mutations do not. Other structures suppress selection, ... More
Critical percolation and A+B --> 2A dynamicsJun 03 2019We study an interacting particle system in which moving particles activate dormant particles linked by the components of critical bond percolation. Addressing a conjecture from Beckman, Dinan, Durrett, Huo, and Junge for a continuous variant, we prove ... More
Joint CLT for top eigenvalues of sample covariance matrices of separable high dimensional long memory processesJun 03 2019For $N,n\in\mathbb{N}$, consider the sample covariance matrix $$S_N(T)=\frac{1}{N}XX^*$$ from a data set $X=C_N^{1/2}ZT_n^{1/2}$, where $Z=(Z_{i,j})$ is a $N\times n$ matrix having i.i.d. entries with mean zero and variance one, and $C_N, T_n$ are deterministic ... More
Bayesian Game of Locks, Bombs and TestingJun 03 2019We consider the game with discrete units of resources for protection and destruction of some sites. In our model, Defender (DF) has locks and Attacker (AT) has bombs to allocate among sites, trying to destroy these sites. One or more bombs can be placed ... More