Random walks in a quarter plane with zero drifts. I. Ergodicity and null recurrence
Random walks in random medium on Z and Lyapunov spectrum
Random walks on graphs with volume and time doubling.
This paper studies the on- and off-diagonal upper estimate and the two-sided transition probability estimate of random walks on weighted graphs.
Random walks on groups and monoids with a Markovian harmonic measure.
Random walks on trees and matchings.
Rapid mixing of Swendsen-Wang dynamics in two dimensions [Book]
Rate of escape of the mixer chain.
Récurrence des librairies sur un arbre
Recurrence for branching Markov chains.
Recurrent graphs where two independent random walks collide finitely often.
Reduction of absorbing Markov chain
In this paper we consider an absorbing Markov chain with finite number of states. We focus especially on random walk on transient states. We present a graph reduction method and prove its validity. Using this method we build algorithms which allow us to determine the distribution of time to absorption, in particular we compute its moments and the probability of absorption. The main idea used in the proofs consists in observing a nondecreasing sequence of stopping times. Random walk on the initial...
Regeneration and general Markov chains.
Régularité des matrices à diagonale dominante. Applications à l'absorption dans les chaînes et processus de Markov
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.
Relative stability and weak convergence in non-decreasing stochastically monotone Markov chains.
Remarks on intersection-equivalence and capacity-equivalence
Remarques sur l'hypercontractivité et l'évolution de l'entropie pour des chaînes de Markov finies
Robust mixing.
Sampling the Fermi statistics and other conditional product measures
Through a Metropolis-like algorithm with single step computational cost of order one, we build a Markov chain that relaxes to the canonical Fermi statistics for k non-interacting particles among m energy levels. Uniformly over the temperature as well as the energy values and degeneracies of the energy levels we give an explicit upper bound with leading term km ln k for the mixing time of the dynamics. We obtain such construction and upper bound as a special case of a general result on (non-homogeneous)...
Self-normalized large deviations for Markov chains.