We construct a Riemannian manifold where the Kendall-Cranston coupling of two Brownian particle does not maximize the coupling probability.

A Central Limit Theorem for non-commutative random variables is proved using the Lindeberg method. The theorem is a generalization of the Central Limit Theorem for free random variables proved by Voiculescu. The Central Limit Theorem in this paper relies on…

We present a short probabilistic proof of a weak convergence result for the number of cuts needed to isolate the root of a random recursive tree. The proof is based on a coupling related to a certain random walk.

The central limit theorem for the product of sums of various random variables has been studied in a variety of settings. The purpose of this note is to show that this kind of result is a corollary of the invariance…

We show that any element from the ($L^2$-)maximal domain of a jump-type symmetric Dirichlet form can be approximated by test functions under some conditions. This gives us a direct proof of the fact that the test functions is dense in…

By means of a simple conditioning/comparison argument, we derive the chance of a long lifetime for Brownian motion in a horn-shaped domain.

This note answers one question in [1] concerning the connected allocation for the Poisson process in $\mathbb{R}^2$. The proposed solution makes use of the Riemann map from the plane minus the minimal spanning forest of the Poisson point process to…

We show how the evolving set methodology of Morris and Peres can be used to show Cheeger inequalities for bounding the spectral gap of a finite Markov kernel. This leads to sharp versions of several previous Cheeger inequalities, including ones…

Let $\{X, X_{{n}}; n\in\mathbb{N}^{d}\}$ be a field of i.i.d. random variables indexed by $d$-tuples of positive integers and let $S_{{n}}=\sum_{{k}\leq{n}}X_{{k}}$. We prove some strong limit theorems for $S_{{n}}$. Also, when $d\geq 2$ and $h({n})$ satisfies some conditions, we show that…

We prove that the expected Lebesgue measure of the range of an additive Levy process is positive if and only if the product $\Re([1+\Psi_1(\xi)]^{-1})...\Re([1+\Psi_N(\xi)]^{-1})$ is integrable. This was previously proved by Khoshnevisan, Xiao and Zhong [1] under a sector condition.