We give a short proof of Theorem 1.2 (i) from the paper "The Alexander-Orbach conjecture holds in high dimensions" by G. Kozma and A. Nachmias. We show that the expected size of the intrinsic ball of radius $r$ is at…

We present functional versions of recent results on the univariate distributions of the process $V_{x,u} = x + W_{u\tau(x)},$ $0\le u\le 1$, where $W_\bullet$ is the standard Brownian motion process, $x>0$ and $\tau (x) =\inf\{t>0 :\, W_{t}=-x\}$.

In this note we explain two transitions known for moment generating functions of local times by means of properties of the renewal measure of a related renewal equation. The arguments simplify and strengthen results on the asymptotic behavior in the…

We present a detailed proof of the Dovbysh-Sudakov representation for symmetric positive definite weakly exchangeable infinite random arrays, called Gram-de Finetti matrices, which is based on the representation result of Aldous and Hoover for arbitrary (not necessarily positive definite) symmetric…

In this article, we consider a stationary array of random variables (which satisfy some asymptotic independence conditions), and the corresponding sequence of point processes. Our main result identifies some explicit conditions for the convergence of the sequence of point processes…

In this paper the question of the extent to which truncated heavy tailed random vectors, taking values in a Banach space, retain the characteristic features of heavy tailed random vectors, is answered from the point of view of the central…

In this paper we deal with Mellin convolution of generalized Gamma densities which leads to integrals of modified Bessel functions of the second kind. Such convolutions allow us to explicitly write the solutions of the time-fractional diffusion equations involving the…

This paper presents a very simple and self-contained proof of disorder irrelevance for inhomogeneous pinning models with return exponent $\alpha \in (0,1/2)$. We also give a new upper bound for the contact fraction of the disordered model at criticality.

The purpose of this note is to prove a central limit theorem for the third integrated moment of the Brownian local time increments using techniques of stochastic analysis. The main ingredients of the proof are an asymptotic version of Knight's…

We first give an example of a negatively associated measure which does not satisfy the van den Berg-Kesten inequality. Next we show that the class of measures satisfying the van den Berg-Kesten inequality is not closed under either of conditioning,…