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.
Exact closed form of the return probability on the Bethe lattice
GIACOMETTI, Achille
1995-01-01
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.File in questo prodotto:
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