Recurrent graphs where two independent random walks collide finitely often Manjunath Krishnapur and Yuval Peres
نویسندگان
چکیده
We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely. In particular, the comb lattice, obtained from Z 2 by removing all horizontal edges off the x-axis, has this property. We also conjecture that the same property holds for some other graphs, including the incipient infinite cluster for critical percolation in Z 2 .
منابع مشابه
Recurrent graphs where two independent random walks collide finitely
We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely. In particular, the comb lattice, obtained from Z 2 by removing all horizontal edges off the x-axis, has this property. We also conjecture that the same property holds for some other graphs, including the incipient infinite cluster for critical percolation ...
متن کاملCollisions of Random Walks
A recurrent graph G has the infinite collision property if two independent random walks on G, started at the same point, collide infinitely often a.s. We give a simple criterion in terms of Green functions for a graph to have this property, and use it to prove that a critical Galton-Watson tree with finite variance conditioned to survive, the incipient infinite cluster in Z with d ≥ 19 and the ...
متن کاملZeros of Gaussian Analytic Functions and Determinantal Point Processes
Contents Preface vii Chapter 1. Introduction 1 1.1. Random polynomials and their zeros 1 1.2. Basic notions and definitions 6 1.3. Hints and solutions 11 Chapter 2. Gaussian Analytic Functions 13 2.
متن کاملDeterminantal Processes and Independence
Abstract: We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees). They have the striking property that the number of points in a region D is a sum of independent Bernoulli random variables, with parameters which a...
متن کاملLocalization for controlled random walks and martingales
We consider controlled random walks that are martingales with uniformly bounded increments and nontrivial jump probabilities and show that such walks can be constructed so that P (Su n = 0) decays at polynomial rate n where α > 0 can be arbitrarily small. We also show, by means of a general delocalization lemma for martingales, which is of independent interest, that slower than polynomial decay...
متن کامل