Markov chain intersections and the loop-erased walk

Russell Lyons; Yuval Peres; Oded Schramm

Displaying similar documents to “Markov chain intersections and the loop-erased walk”

Limit theorems for one-dimensional transient random walks in Markov environments

Eddy Mayer-Wolf, Alexander Roitershtein, Ofer Zeitouni (2004)

Annales de l'I.H.P. Probabilités et statistiques

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The infinite valley for a recurrent random walk in random environment

Nina Gantert, Yuval Peres, Zhan Shi (2010)

Annales de l'I.H.P. Probabilités et statistiques

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We consider a one-dimensional recurrent random walk in random environment (RWRE). We show that the – suitably centered – empirical distributions of the RWRE converge weakly to a certain limit law which describes the stationary distribution of a random walk in an infinite valley. The construction of the infinite valley goes back to Golosov, see (1984) 491–506. As a consequence, we show weak convergence for both the maximal local time and the self-intersection local time...

Loop-free Markov chains as determinantal point processes

Alexei Borodin (2008)

Annales de l'I.H.P. Probabilités et statistiques

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We show that any loop-free Markov chain on a discrete space can be viewed as a determinantal point process. As an application, we prove central limit theorems for the number of particles in a window for renewal processes and Markov renewal processes with Bernoulli noise.

Unpredictability of the occurrence time of a long laminar period in a model of temporal intermittency

P. Collet, A. Galves, B. Schmitt (1992)

Annales de l'I.H.P. Physique théorique

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Average properties of random walks on Galton-Watson trees

Dayue Chen (1997)

Annales de l'I.H.P. Probabilités et statistiques

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