A 0-1 law for vertex-reinforced random walks on Z with weight of order k(alpha), alpha < 1/2

作者：Schapira Bruno^*

来源：Electronic Communications in Probability, 2012, 17: 1-8.

DOI：10.1214/ECP.v17-2084

• Self-interacting random walk
• Reinforced random walk
• 0-1 law

We prove that Vertex Reinforced Random Walk on Z with weight of order k(alpha), with alpha is an element of [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.

• 出版日期2012-6-13