A $0-1$ law for vertex-reinforced random walks on $mathbb{Z}$ with weight of order $k^alpha$, $alphaReport as inadecuate




A $0-1$ law for vertex-reinforced random walks on $mathbb{Z}$ with weight of order $k^alpha$, $alpha - Download this document for free, or read online. Document in PDF available to download.

1 LM-Orsay - Laboratoire de Mathématiques d-Orsay

Abstract : We prove that Vertex Reinforced Random Walk on $\mathbb{Z}$ with weight of order $k^\alpha$, with $\alpha\in 0,1-2$, is either almost surely recurrent or almost surely transient. This improves a previous result of Volkov who showed that the set of sites which are visited infinitely often was a.s. either empty or infinite.

Keywords : 0-1 law Vertex Reinforced Random Walk 0-1 law.





Author: Bruno Schapira -

Source: https://hal.archives-ouvertes.fr/



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