Gaussian lower bounds for random walks from elliptic regularity
Generic result for the existence of a free semi-group
Geodesics and recurrence of random walks in disordered systems.
Geometric ergodicity for a class of Markov chains
Geometric infinite divisibility, stability, and self-similarity: an overview
The concepts of geometric infinite divisibility and stability extend the classical properties of infinite divisibility and stability to geometric convolutions. In this setting, a random variable X is geometrically infinitely divisible if it can be expressed as a random sum of components for each p ∈ (0,1), where is a geometric random variable with mean 1/p, independent of the components. If the components have the same distribution as that of a rescaled X, then X is (strictly) geometric stable....
Geometric Stable Laws Through Series Representations
Let (Xi ) be a sequence of i.i.d. random variables, and let N be a geometric random variable independent of (Xi ). Geometric stable distributions are weak limits of (normalized) geometric compounds, SN = X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain series representation of the limiting geometric stable distribution. In addition, we study the asymptotic...
Giant component and vacant set for random walk on a discrete torus
We consider random walk on a discrete torus of side-length , in sufficiently high dimension . We investigate the percolative properties of the vacant set corresponding to the collection of sites which have not been visited by the walk up to time . We show that when is chosen small, as tends to infinity, there is with overwhelming probability a unique connected component in the vacant set which contains segments of length const . Moreover, this connected component occupies a non-degenerate...
Giant vacant component left by a random walk in a random d-regular graph
We study the trajectory of a simple random walk on a d-regular graph with d ≥ 3 and locally tree-like structure as the number n of vertices grows. Examples of such graphs include random d-regular graphs and large girth expanders. For these graphs, we investigate percolative properties of the set of vertices not visited by the walk until time un, where u > 0 is a fixed positive parameter. We show that this so-called vacant set exhibits a phase transition in u in the following sense: there...
Grandes déviations pour un système hydrodynamique asymétrique de particules indépendantes
Green functions for killed random walks in the Weyl chamber of Sp(4)
We consider a family of random walks killed at the boundary of the Weyl chamber of the dual of Sp(4), which in addition satisfies the following property: for any n ≥ 3, there is in this family a walk associated with a reflection group of order 2n. Moreover, the case n = 4 corresponds to a process which appears naturally by studying quantum random walks on the dual of Sp(4). For all the processes belonging to this family, we find the exact asymptotic of the Green functions along all infinite paths...
Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel–Leader graphs
Groupes aléatoires
Quelles sont les propriétés d’un groupe de présentation finie “tiré au hasard” ? La réponse à cette question dépend bien entendu de la méthode choisie pour le tirage au sort. On peut par exemple fixer générateurs et choisir relations aléatoirement parmi les mots de longueur , puis faire tendre vers l’infini. On peut aussi choisir un graphe fini, étiqueter aléatoirement ses arêtes par des générateurs, et considérer le groupe engendré par ces générateurs, soumis aux relations lues sur les cycles...