概率论

We first establish strong convergence rates for multiscale systems driven by $\alpha$-stable processes, with analyses constructed in two distinct scaling regimes. When addressing weak convergence rates of this system, we derive four…

We prove an inequality for the spectral norm of matrix valued stochastic integrals. This inequality can be seen either as a non-commutative version of the Burkholder-Davis-Gundy inequality or as an extension of the non-commutative…

We study a mutliscale jump process introduced in a work by Crudu, Debussche, Muller and Radulescu. Using an adequate coupling, we are able to prove the strong convergence, for the uniform topology, to a piecewise deterministic Markov…

We introduce a new methodology for modeling regular spatial data using hyperuniform point processes. We show that, under some mixing conditions on the perturbations, perturbed lattices in general dimension are hyperuniform. Due to their…

We establish a formula for moments of certain random variables involving positive continuous additive functionals (PCAFs) of standard processes which have absolutely continuous transition functions and are in duality with standard processes…

In this note, we investigate Bernoulli oriented bond percolation with parameter $p$ on $\mathbb{Z}^2$. In addition to the standard edges, which are open with probability $p$, we introduce diagonal edges each open with probability…

We show how the flow approach of Duch, with elementary differentials as coordinates, can be used to prove well-posedness for rough stochastic differential equations driven by fractional Brownian motion with Hurst index $H > \frac{1}{4}$. A…

We study the sensitivity of the eigenvectors of random matrices, showing that even small perturbations make the eigenvectors almost orthogonal. More precisely, we consider two deformed Wigner matrices $W+D_1$, $W+D_2$ and show that their…

We prove that under the Brownian evolution on large non-Hermitian matrices the log-determinant converges in distribution to a 2+1 dimensional Gaussian field in the Edwards-Wilkinson regularity class, namely it is logarithmically correlated…

At high temperature, the overlap of two particles chosen independently according to the Gibbs measure of the branching Brownian motion converges to zero as time goes to infinity. We investigate the precise decay rate of the probability to…

We consider the problem of recovering the community structure in the stochastic block model. We aim to describe the mutual information between the observed network and the actual community structure as the number of nodes diverges while the…

We introduce the concept of an imprecise Markov semigroup \(\mathbf Q\). It is a tool that allows us to represent ambiguity around both the transition probabilities and the invariant measure of a continuous-time Markov process via a…

We establish a connection between tagged particles and size-biased empirical processes in interacting particle systems, in analogy to classical results on the propagation of chaos. In a mean-field scaling limit, the evolution of the…

We study preferential attachment models where vertices enter the network with i.i.d. random numbers of edges that we call the out-degree. We identify the local limit of such models, substantially extending the work of Berger et al.(2014).…

We propose a new computational framework for the expected number of real roots of a stochastic function on a given interval. The classical Kac-Rice formula requires the joint density of the function and its derivative, which is often…

We develop a general framework for the probabilistic analysis of random finite point clouds in the context of topological data analysis. We extend the notion of a barcode of a finite point cloud to compact metric spaces. Such a barcode…

We study a family of (multivariate-)Gaussian Hamiltonian Monte Carlo (GHMC) operators and prove that the family of Gaussian distributions and their mixtures are invariant under such operators. Furthermore, each such operator is a…

We study the rough-smooth boundary in the two-periodic Aztec diamond, a random domino tiling model exhibiting three types of macroscopic regions. We show that the height function at this boundary converges to an independent sum of an Airy…

We consider a probabilistic cellular automaton (PCA) of evaporation-deposition on the one-dimensional lattice having $n$ sites with periodic boundary conditions, in which each site, during each epoch, can be in one of two states: $0$ and…

We prove that the free energy of the half-space log-gamma polymer $N^{2/3+\delta}$ away from the boundary in the non-attractive regime converges to the directed landscape. Based on the convergence of the full-space log-gamma free energy to…