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Exact clesed form of the return probability on the Bethe lattice

Achille Giacometti
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Abstract

An exact closed form solution for the return probability of a random walk on the Bethe lattice is given. The long-time asymptotic form confirms a previously known expression. It is however shown that this exact result reduces to the proper expression when the Bethe lattice degenerates on a line, unlike the asymptotic result which is singular. This is shown to be an artefact of the asymptotic expansion. The density of states is also calculated.

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Achille Giacometti. 1994-11-28. Exact clesed form of the return probability on the Bethe lattice. https://doi.org/10.1088/0305-4470%2F28%2F1%2F003

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