Exact clesed form of the return probability on the Bethe lattice

Details Exact clesed form of the return probability on the Bethe lattice Exact clesed form of the return probability on the Bethe lattice

1994-11-28

arxiv.org/abs/cond-mat/9411113v1

Physics

Condensed Matter

7 pages, RevTex 3.0, 2 figures available upon request from agiacom@iff042.iff.kfa-juelich.de, to be published in J.Phys.A Lett

Scientific paper

10.1088/0305-4470/28/1/003

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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