Random walks on infinite self-similar graphs.
Random walks on the affine group of local fields and of homogeneous trees
The affine group of a local field acts on the tree (the Bruhat-Tits building of ) with a fixed point in the space of ends . More generally, we define the affine group of any homogeneous tree as the group of all automorphisms of with a common fixed point in , and establish main asymptotic properties of random products in : (1) law of large numbers and central limit theorem; (2) convergence to and solvability of the Dirichlet problem at infinity; (3) identification of the Poisson boundary...
Random walks that avoid their past convex hull.
Random walks with -wise independent increments.
Randomly Weighted Series of Contractions in Hilbert Spaces.
Réarrangements convexes des marches aléatoires
Recorridos aleatorios simples en tiempo continuo.
The properties of a certain generalization of simple random walk to continuous time are analyzed in this paper. After the definition, its transition probabilities, and the differential equations satisfied by those, are obtained. Under some conditions, the convergence of this random walk to a Wiener process is then established. Finally, absorption probabilities and mean times until absorption are calculated, giving some insight into the behaviour of the process.
Recurrence and transience of excited random walks on and strips.
Recurrence and transience of the edge graph of a tiling of the euclidean plane.
Récurrence des librairies sur un arbre
Récurrence des marches aléatoires et ergodicité du flot géodésique sur les graphes réguliers.
Recurrence of reinforced random walk on a ladder.
Recurrent graphs where two independent random walks collide finitely often.
Recurrent Random Walks and Invariant Measures on Semigroups of n x n Matrices.
Refinement type equations: sources and results
It has been proved recently that the two-direction refinement equation of the form can be used in wavelet theory for constructing two-direction wavelets, biorthogonal wavelets, wavelet packages, wavelet frames and others. The two-direction refinement equation generalizes the classical refinement equation , which has been used in many areas of mathematics with important applications. The following continuous extension of the classical refinement equation has also various interesting applications....
Régularité du plus grand exposant caractéristique des produits de matrices aléatoires indépendantes et applications
Reinforced walk on graphs and neural networks
A directed-edge-reinforced random walk on graphs is considered. Criteria for the walk to end up in a limit cycle are given. Asymptotic stability of some neural networks is shown.
Remarks on intersection-equivalence and capacity-equivalence
Remarks on random walks on semi simple Lie groups
Remarque sur l'uniforme sommabilité des suites de variables aléatoires à valeurs vectorielles normées