概率论

We prove that a sum of random matrices generated by a $\psi$-mixing Markov chain has similar spectral properties to a Gaussian matrix with the same mean and covariance structure. This nonasymptotic universality principle enables sharp…

Laplace-type results characterize the limit of sequence of measures $(\pi_\varepsilon)_{\varepsilon >0}$ with density w.r.t the Lebesgue measure $(\mathrm{d} \pi_\varepsilon / \mathrm{d} \mathrm{Leb})(x) \propto \exp[-U(x)/\varepsilon]$…

We study the behaviour of four spins systems (the XY model, the Villain model, the XY height function and the integer-valued Gaussian free field) in the presence of a non-elliptic quenched disorder. In the article [DG25], it was shown that…

In a seminal work, Chatterjee and Durrett (2009) established that for the SIS epidemic process on random graphs with power-law degree distributions, the infection survives for an exponentially long time (in the network size) for any fixed,…

We prove the existence of the local limit of uniform random d-regular bipartite planar maps, for every $d\geq 3$, as the number of vertices tends to infinity. The proof relies on a bijection between maps and so-called blossoming trees…

In the article, we address the problem of absolute continuity of translated Rosenblatt measures on the path space. In [\v{C}oupek, P., K\v{r}\'i\v{z}, P., Maslowski, B., Stoch. Proc. Appl. 179 (2025) art. no. 104499], it is shown that there…

A random geometric graph $G(\mathcal{X}_n, r_n)$ is formed by taking a binomial process $\mathcal{X}_n$ as the set of vertices and joining any two distinct points with an edge if they lie within distance $r_n$ of each other. We investigate…

We study backward stochastic differential equations (BSDEs) in infinite horizon and design efficient numerical schemes for solving them. We establish a probabilistic representation of the solution of the BSDE using Malliavin derivative and…

We prove the existence of weak solutions for distribution-dependent stochastic Volterra equations under linear growth and continuity conditions on the coefficients and mild regularity assumptions on the kernels, including singular kernels.…

We study stochastic differential equations driven by finite-order chaos processes on abstract Wiener spaces, with pathwise Riemann-Stieltjes integration. The driving noise is an $\mathbb{R}^m$-valued chaotic process given by multiple…

In this work, we derive a complete characterization of all ruin-inducing probability measures that preserve the structure of a given compound renewal process in terms of suitable pairs of functions $(\gamma,\delta)$. This result allows us…

In this paper, we accelerate Langevin Monte Carlo sampling from Gibbs measures $\pi\propto \exp(-U)$ by adding a large drift that preserves the invariant measure. For warm-start initial data, we characterize the sharp asymptotic decay rate…

The random transposition shuffle on repeated cards induces a Markov chain on the quotient space of arrangements with multiplicities, and is equivalent to the many-urn mean-field Bernoulli-Laplace model introduced by Scarabotti. Writing…

We construct a family of velocity fields demonstrating the sharpness of the classical Zvonkin--Veretennikov--Davie strong well-posedness by noise regime. We consider stochastic differential equations driven by Brownian noise with drift $u$…

Kac's walk on the rotation group, introduced by Hastings in 1970, is an important high-dimensional Markov chain with applications in statistical physics, statistics, cryptography, and computational science. Despite its simple transition…

We prove explicit finite-$N$ lower bounds for $\mathbb P(\bigcup_{k=1}^N A_k)$ when the $\sigma$-algebras generated by an event sequence satisfy quantitative $\varphi$- or $\alpha$-mixing bounds. The main $\varphi$-mixing estimate is…

We study Mallows random permutations conditioned to avoid a given pattern $\alpha$ of length~$3$. When the bias parameter is of the form $e^{\beta/n}$, we prove that these permutations converge to a non-trivial explicit deterministic…

In this paper, we study the doubly reflected backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs for short) when the generator has quadratic growth in the $z$-component. Based on the theory of $G$-BMO…

This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…

This paper considers the mean waiting times in discrete-time preemptive-resume and nonpreemptive priority single-server queues fed by K independent batch Markovian arrival streams with geometrically distributed idle periods. While being…