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.
Plumes in kinetic transport: how the simple random walk can be too simple
Favourite sites of simple random walk
The Beurling estimate for a class of random walks
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