Upper bound on the disconnection time of discrete cylinders and random interlacements

Sznitman, Alain-Sol

Ann. Probab., Tome 37 (2009) no. 1, p. 1715-1746 / Harvested from Project Euclid

Résumé

We study the asymptotic behavior for large N of the disconnection time T_N of a simple random walk on the discrete cylinder (ℤ/Nℤ)^d×ℤ, when d≥2. We explore its connection with the model of random interlacements on ℤ^d+1 recently introduced in [Ann. Math., in press], and specifically with the percolative properties of the vacant set left by random interlacements. As an application we show that in the large N limit the tail of T_N/N^2d is dominated by the tail of the first time when the supremum over the space variable of the Brownian local times reaches a certain critical value. As a by-product, we prove the tightness of the laws of T_N/N^2d, when d≥2.

Publié le : 2009-09-15
Classification: Disconnection, random walks, random interlacements, discrete cylinders, 60G50, 60K35, 82C41

@article{1253539855,
     author = {Sznitman, Alain-Sol},
     title = {Upper bound on the disconnection time of discrete cylinders and random interlacements},
     journal = {Ann. Probab.},
     volume = {37},
     number = {1},
     year = {2009},
     pages = { 1715-1746},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1253539855}
}

Sznitman, Alain-Sol. Upper bound on the disconnection time of discrete cylinders and random interlacements. Ann. Probab., Tome 37 (2009) no. 1, pp.  1715-1746. http://gdmltest.u-ga.fr/item/1253539855/