![](images/spacer.gif) |
|
|
| | | | | |
|
|
|
|
|
Random walk on a discrete torus and random interlacements
|
David Windisch, ETH Zurich |
Abstract
We investigate the relation between the local picture left by the trajectory of a simple random walk on the torus (Z/NZ)d, d ≥ 3, until u Nd time steps, u > 0, and the model of random interlacements recently introduced by Sznitman. In particular, we show that for large N, the joint distribution of the local pictures in the neighborhoods of finitely many distant points left by the walk up to time u Nd converges to independent copies of the random interlacement at level u.
|
Full text: PDF
Pages: 140-150
Published on: March 10, 2008
|
Bibliography
-
D.J. Aldous. Probability Approximations via the Poisson Clumping Heuristic. Springer-Verlag, 1989.
Math. Review 90k:60004
-
D.J. Aldous and M. Brown. Inequalities for rare events in time-reversible Markov chains I. Stochastic Inequalities. M. Shaked and Y.L. Tong, ed., IMS Lecture Notes in Statistics, volume 22, 1992.
Math. Review 94g:60132
-
D.J. Aldous and J. Fill. Reversible Markov chains and random walks on graphs. http://www.stat.berkeley.edu/~aldous/RWG/book.html.
-
I. Benjamini, A.S. Sznitman. Giant component and vacant set for random walk on a discrete torus. J. Eur. Math. Soc.~(JEMS) , 10(1):133-172, 2008.
-
R. Durrett. Probability: Theory and Examples. (third edition) Brooks/Cole, Belmont, 2005.
-
G.F. Lawler. Intersections of random walks. Birkhäuser, Basel, 1991.
Math. Review 92f:60122
-
L. Saloff-Coste. Lectures on finite Markov chains, volume 1665. Ecole d'Eté de Probabilités de Saint Flour, P. Bernard, ed., Lecture Notes in Mathematics, Springer, Berlin, 1997
Math. Review 99b:60119
-
P.M. Soardi. Potential Theory on Infinite Networks. Springer-Verlag, Berlin, Heidelberg, New York, 1994.
Math. Review 96i:31005
-
A.S. Sznitman. Vacant set of random interlacements and percolation, preprint, available at http://www.math.ethz.ch/u/sznitman/preprints and http://arxiv.org/abs/0704.2560.
-
A.S. Sznitman. Random walks on discrete cylinders and random interlacements, preprint, available at http://www.math.ethz.ch/u/sznitman/preprints.
|
|
|
|
|
|
|
| | | | |
Electronic Communications in Probability. ISSN: 1083-589X |
|