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A special set of exceptional times for dynamical random walk on $Z^2$

   
@article{EJP571,
	author = {Gideon Amir and Christopher Hoffman},
	title = {A special set of exceptional times for dynamical random walk on $Z^2$},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {13},
	year = {2008},
	keywords = {Random Walks; Dynamical Random Walks, Dynamical Sensativity},
	abstract = {In [2] Benjamini, Haggstrom, Peres and Steif introduced the model of dynamical random walk on the $d$-dimensional lattice $Z^d$. This is a continuum of random walks indexed by a time parameter $t$. They proved that for dimensions $d=3,4$ there almost surely exist times $t$ such that the random walk at time $t$ visits the origin infinitely often, but for dimension 5 and up there almost surely do not exist such $t$. Hoffman showed that for dimension 2 there almost surely exists $t$ such that the random walk at time $t$ visits the origin only finitely many times [5]. We refine the results of [5] for dynamical random walk on $Z^2$, showing that with probability one the are times when the origin is visited only a finite number of times while other points are visited infinitely often.},
	pages = {no. 63, 1927-1951},
	issn = {1083-6489},
	doi = {10.1214/EJP.v13-571},    
        url = {http://ejp.ejpecp.org/article/view/571}}