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On the internal distance in the interlacement set

   
@article{EJP1936,
	author = {Jiří Černý and Serguei Popov},
	title = {On the internal distance in the interlacement set},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {17},
	year = {2012},
	keywords = {Random interlacement; Internal distance; Shape theorem;   Simple random walk; Capacity},
	abstract = {We prove a shape theorem for the internal (graph) distance on the interlacement set $\mathcal{I}^u$ of the random interlacement model on $\mathbb Z^d$, $d\ge 3$. We provide large deviation estimates for the internal distance of distant points in this set, and use these estimates to study the internal distance on the range of a simple random walk on a discrete torus.

},
	pages = {no. 29, 1-25},
	issn = {1083-6489},
	doi = {10.1214/EJP.v17-1936},    
        url = {http://ejp.ejpecp.org/article/view/1936}}