2006/09/10 by Gideon Amir, Amir, Gideon, Christopher Hoffman +1
Mathematics · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Mathematical Dynamics and Fractals #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.math/0609267
Benjamini,Haggstrom, Peres and Steif introduced the model of dynamical random walk on Zd. This is a continuum of random walks indexed by a parameter t. They proved that for d=3,4 there almost surely exist t such that the random walk at time t visits the origin infinitely often, but for d > 4 there almost surely do not exist such t. Hoffman showed that for d=2 there almost surely exists t such that the random walk at time t visits the origin only finitely many times. We refine the results of Hoffman for dynamical random walk on Z2, showing that with probability one there are times when the origin is visited only a finite number of times while other points are visited infinitely often.