Nadine Guillotin-Plantard

TL;DR: In this article, a central limit theorem for quantum random walks on lattices has been proved for the case where only one Gaussian distribution appears in the limit, where the quantum random walk is a quantum generalization of Markov chains on finite graphs.

TL;DR: In this paper, the authors considered the problem of quantum Markov chains on finite graphs or on lattices and obtained a Central Limit Theorem with explicit drift and explicit covariance matrix for the case where only one Gaussian distribution appears in the limit.

Abstract: The aim of this paper is to present a result of discrete approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known on the context in which such processes can arise. To our knowledge, discretisation and convergence theorems are available only in the case of stable Levy motions and fractional Brownian motions. This paper yields new results in this direction. Our main result is the convergence of the random rewards schema, which was firstly introduced by Cohen and Samorodnitsky, and that we consider in a more general setting. Strong relationships with Kesten and Spitzer's random walk in random sceneries are evidenced. Finally, we study some path properties of the limit process.

TL;DR: In this paper, the authors considered the case of random walks on randomly oriented lattices and proved the convergence in distribution when the index of the stable laws is fixed, and they showed that the convergence can be computed as a function of the number of i.i.d. random variables.

TL;DR: In this paper, Wahrsch and Gebiete prouvons la convergence en loi and un theoreme limite local quand α=d$ (i.i.d.