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In this talk we discuss a notion of $\psi$-Dirichlet in Diophantine approximation which concerns improving Dirichlet’s approximation theorem to a general approximating function $\psi$. This notion was...
We prove that a recurrent random walk (RW) in i.i.d. random environment (RE) on a strip which does not obey the Sinai law exhibits the Central Limit asymptotic behaviour.
We consider excited random walk on a strip. We assume that the cookies are positive and that the total expected drift per site is less than 1/L where L is the width of the strip. We prove a quenched...
We prove a local limit the sums of independent random vectors satisfying appropriate tightness assumptions. In particular, the local limit theorem holds in dimension 1 if the summands are uniformly bo...
We consider the evolution of a connected set on the plane carried by a space periodic incompressible stochastic flow. While for almost every realization of the stochastic flow at time t ...
We consider the evolution of a connected set on the plane carried by a space periodic incompressible stochastic flow. While for almost every realization of the stochastic flow at time t mo...
This paper characterizes mixtures of symmetric location families. More specifically, let X = (XI, Xz, .. . ) be an exchangeable sequence of real-valued random variables. By de Finetti's theorem, X...
This is the the first of a series of papers considering properties of quantum systems over 2D graphs or manifolds, with continuous spins. In the model considered here the phase space of a single spin ...
For a graph $G$, denote by $t(G)$ (resp. $b(G)$) the maximum size of a triangle-free (resp. bipartite) subgraph of $G$. Of course $t(G) \geq b(G)$ for any $G$, and a classic result of Mantel from 1907...
In this paper, we study the complex Wigner matrices $M_n=\frac{1}{\sqrt{n}}W_n$ whose eigenvalues are typically in the interval $[-2,2]$. Let $\lambda_1\leq \lambda_2...\leq\lambda_n$ be the ordered e...
We show that, under certain smoothness conditions, a Brownian martingale at a fixed time can be represented as an exponential of its value at a later time. The time-dependent generator of this exponen...
We prove a structural result for degree-$d$ polynomials. In particular, we show that any degree-$d$ polynomial, $p$ can be approximated by another polynomial, $p_0$, which can be decomposed as some fu...
In this paper,in the base of sublinear expectation space called 'G-expectation space' that introduced by Peng , adapting Peng's IID notion and applying Peng's new CLT under sublinear expectations, we ...
Abstract: We use a Stochastic Differential Equation satisfied by Brownian motion taking values in the unit sphere $S_{n-1}\subset\mathbb{R}^{n}$ and we obtain a Central Limit Theorem for a sequence of...
Abstract: In a recent paper, Michalowicz et al. provide an extension of Isserlis theorem to the case of a Bernoulli location mixture of a Gaussian vector. We extend here this result to the case of any...

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