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Currently displaying 1 – 2 of 2

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Slowdown estimates for ballistic random walk in random environment

Noam Berger — 2012

Journal of the European Mathematical Society

We consider models of random walk in uniformly elliptic i.i.d. random environment in dimension greater than or equal to 4, satisfying a condition slightly weaker than the ballisticity condition $(T^{'})$ . We show that for every $ϵ > 0$ and $n$ large enough, the annealed probability of linear slowdown is bounded from above by $exp (- {(log n)}^{d - ϵ})$ . This bound almost matches the known lower bound of $exp (- C {(log n)}^{d})$ , and signiﬁcantly improves previously known upper bounds. As a corollary we provide almost sharp estimates for the quenched probability...

Transience of percolation clusters on wedges.

Angel, Omer; Benjamini, Itai; Berger, Noam; Peres, Yuval — 2006

Electronic Journal of Probability [electronic only]

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