概率论

This paper presents a detailed study of constrained quantization for both finite and infinite discrete probability distributions supported on subsets of the real line. Under specific geometric constraints - namely, a semicircular arc and…

Consider a subcritical branching Markov chain. Let $Z_n$ denote the counting measure of particles of generation $n$. Under some conditions, we give a probabilistic proof for the existence of the Yaglom limit of $(Z_n)_{n\in\mathbb{N}}$ by…

A \emph{random temporal graph} is an Erd\H{o}s-R\'enyi random graph $G(n,p)$, together with a random ordering of its edges. A path in the graph is called \emph{increasing} if the edges on the path appear in increasing order. A set $S$ of…

We show that on every affine Weyl group natural random walks are noise sensitive in total variation.

We initiate a study of large deviations for block model random graphs in the dense regime. Following Chatterjee-Varadhan(2011), we establish an LDP for dense block models, viewed as random graphons. As an application of our result, we study…

Let $P_n(x) = \sum_{k=0}^{n} \xi_k x^k$ be a Kac random polynomial, where the coefficients $\xi_k$ are i.i.d.\ copies of a given random variable $\xi$. Based on numerical experiments, it has been conjectured that if $\xi$ has mean zero,…

We model the scrambling of a Rubik's cube by a Markov chain and introduce a stopping time $T$ which is a quite natural candidate to be a strong uniform time. This may pave the way for estimating the number of moves required to scramble a…

Bayesian diversity estimators are martingales converging almost surely and in mean with common limit and local behavior with plug in estimators.

By imposing an additional integrability condition on the first component of the solution, this paper establishes an existence and uniqueness result for $L^1$ solutions of multidimensional backward stochastic differential equations (BSDEs)…

We provide non-asymptotic error bounds in the path Wasserstein distance with quadratic integral cost between suitable functionals of the telegraph process and the corresponding functional of Brownian motion with explicit diffusivity…

We study a class of Tricomi-type partial differential equations previously investigated in [28]. Firstly, we generalize the representation formula for the solution obtained there by allowing the coefficient in front of the second-order…

In this paper, a divergence-type integral of a random integrand with respect to the Hermite process of order $k\in\mathsf{N}$ with Hurst parameter $H\in (1/2,1)$ is defined and it is shown that the integral is of finite $1/H$-variation.

This paper deals into the long-term behavior of subordinated critical branching processes with migration. We focus on scenarios where emigration is the dominant factor and introduce additional randomness in timing through a subordination…

Based on a study of a formula representing submodular set function as a supremum of measures dominated by the set function, we present a corresponding formula for a Choquet integration with respect to the set function, on a measurable space…

We show that the critical density for activated random walk on $\mathbb{Z}^d$ approaches the sleep probability as $d \to \infty$ and provide the first-order correction.

For $p\in[1,\infty]$, the $\ell^p$ directed spanning forest (DSF) of dimension $d\geq 2$ is an oriented random geometric graph whose vertex set is given by a homogeneous Poisson point process $\mathcal N$ on $\mathbb R^d$ and whose edges…

Let $\Omega_1, \ldots, \Omega_m$ be probability spaces, let $\Omega=\Omega_1 \times \cdots \times \Omega_m$ be their product and let $A_1, \ldots, A_n \subset \Omega$ be events. Suppose that each event $A_i$ depends on $r_i$ coordinates of…

We establish variational principles for the Hausdorff and packing dimensions of a class of statistically self-affine sponges, including in particular fractal percolation sets obtained from Bara\'nski and Gatzouras-Lalley carpets and…

We consider the Wigner minor process, i.e. the eigenvalues of an $N\times N$ Wigner matrix $H^{(N)}$ together with the eigenvalues of all its $n\times n$ minors, $H^{(n)}$, $n\le N$. The top eigenvalues of $H^{(N)}$ and those of its…

In 1999, Benjamini, Lyons, Peres, and Schramm introduced a notion of weighted-amenability for transitive graphs that is equivalent to the amenability of its automorphism group. For unimodular graphs this notion coincides with classical…