Power-law decay of weights and recurrence of the two-dimensional VRJP

2019/11/19 by Kozma, Gady, Peled, Ron · 1 citation
#60K35 #81T60 #FOS: Mathematics #Primary 60K37 #Probability (math.PR) #Secondary 81T25

paper · doi:10.48550/arxiv.1911.08579

Abstract

The vertex-reinforced jump process (VRJP) is a form of self-interacting random walk in which the walker is biased towards returning to previously visited vertices with the bias depending linearly on the local time at these vertices. We prove that, for any initial bias, the weights sampled from the magic formula on a two-dimensional graph decay at least at a power-law rate. Via arguments of Sabot and Zeng, the result implies that the VRJP is recurrent in two dimensions for any initial bias.

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• VRJP recurrence and fractional-moment decay for the \(H^2|2\) model's effective field on the hierarchical lattice

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