Long time behaviour of random walks on the integer lattice

Bartosz Trojan

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arXiv · 1512.09035

Long time behaviour of random walks on the integer lattice

Bartosz Trojan

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Abstract

We consider an irreducible finite range random walk on the $d$-dimensional integer lattice and study asymptotic behaviour of its transition function $p(n; x)$. In particular, for simple random walk our asymptotic formula is valid as long as $n (n - |x|_1)^{-2}$ tends to zero.

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Bartosz Trojan. 2015-12-30. Long time behaviour of random walks on the integer lattice. https://arxiv.org/abs/1512.09035

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