概率论

Consider the well-known Langevin diffusion on $\mathbb{R}^d$ $$\mathrm{d} X_t = -\nabla U(X_t)\,\mathrm{d} t + \sqrt{2}\mathrm{d} B_t, $$ and its Euler-Maruyama discretization given by $$X_{k+1}=X_k-\eta \nabla U(X_k)+\sqrt{2\eta…

We show that tessellations of hyperbolic space by isometry-invariant Poisson processes of $(d-1)$-dimensional hyperplanes do not have an unbounded cell at the critical intensity. This extends a result by Porret-Blanc for the hyperbolic…

Consider a Markov chain $(X_i)_{i\ge0}$ with invariant measure $\mu$ that admits the representation $X_{i+1}=\Phi(X_i,U_i)$, where $(U_i)_{i\ge0}$ are i.i.d. random variables and $\Phi$ is a measurable map. We introduce a tangent-decoupled…

We study a multi-type Ehrenfest process modeled as a finite quasi-birth-death (QBD) process. We assume that the transitions are allowed only to the two adjacent levels of the same phase and are characterized by linear rates. The crucial…

This paper proves a large deviation principle (LDP) for the stationary distribution of queue lengths in a subcritical generalised Jackson network assuming a Cramer condition on the interarrival and service times. The deviation function is…

Both complete decoupling and tangent decoupling are classical tools aiming to compare two random processes where one has a weaker dependence structure. We give a new proof for the complete decoupling inequality, which provides a lower bound…

We study the behavior of log-supermodular functions under convolution. In particular we show that log-concave product densities preserve log-supermodularity, confirming in the special case of the standard Gaussian density, a conjecture of…

This paper is to investigate if the solution of a hybrid stochastic functional differential equation (SFDE) with infinite delay can be approximated by the solution of the corresponding hybrid SFDE with finite delay. A positive result is…

We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…

We consider the stochastic quantization equation associated with the weighted exponential quantum field model (or the H{\o}egh-Krohn model) on the two dimensional torus. Unlike in the case of the usual (unweighted) exponential model, the…

In the 1950s, W. Feller characterized the most general Brownian motion on the closed half-line. He showed that any such process is a mixture of reflected, sticky, and killed Brownian motions. By most general Brownian motion, we mean a…

We present a collection of explicit diffusion approximations to small temperature Schr\"{o}dinger bridges on manifolds. Our most precise results are when both marginals are the same and the Schr\"{o}dinger bridge is on a manifold with a…

The adapted Wasserstein distance $\mathcal{AW}$ is a modification of the classical Wasserstein metric, that provides robust and dynamically consistent comparisons of laws of stochastic processes, and has proved particularly useful in the…

The aim of this expository note is to prove that any $1$-subgaussian random vector is dominated in the convex ordering by a universal constant times a standard Gaussian vector. This strengthens Talagrand's celebrated subgaussian comparison…

We analyze the \emph{equilibrium fluctuations} of a Hamiltonian chain of oscillators on \(\mathbb{Z}\) with an exponential potential, perturbed by a conservative, symmetric noise. Under the canonical \emph{diffusive scaling} \(t \mapsto t…

We prove Berry-Esseen theorems, almost sure invariance principle rates and large deviations for products of independent but not identically distributed invertible matrices with some average (logarithmic) projective contraction and uniform…

We introduce a general framework to show the indistinguishability of infinite clusters (ergodicity of the cluster subrelation) in group-invariant percolation processes with a weaker version of the finite energy property: the possibility of…

Existence and uniqueness of mild solutions to a class of semilinear stochastic evolution equations with additive noise is proved. The linear part of the drift term is the generator of a compact semigroup of contractions, while the nonlinear…

The planar Skorokhod embedding problem was first proposed and solved by R. Gross in 2019 [#gross2019]. Gross worked with probability distributions having finite second moment. In [#boudabra2019remarks, #Boudabra2020], the solutions extended…

We establish sharp large-deviation asymptotic estimates for the maximum order statistic of i.i.d.\ standard normal random variables on all Borel subsets of the positive real line. This result yields more accurate tail approximations than…