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Recurrent Graphs where Two Independent Random Walks Collide Finitely Often

   
@article{ECP1111,
	author = {Manjunath Krishnapur and Yuval Peres},
	title = {Recurrent Graphs where Two Independent Random Walks Collide Finitely Often},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {9},
	year = {2004},
	keywords = {},
	abstract = {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 $Z^2$.},
	pages = {no. 8, 72-81},
	issn = {1083-589X},
	doi = {10.1214/ECP.v9-1111},    
        url = {http://ecp.ejpecp.org/article/view/1111}}