On the recurrence-transience dichotomy for once reinforced random walk

2008. június 24. kedd 16:15

It is well-known that for simple random walk on an infinite, locally finite, connected graph, a random walker either visits every vertex of the graph infinitely often with probability one, no matter where the walker starts, or visits every vertex at most finitely often with probability one, no matter where the walker starts. This is commonly called the recurrence-transience dichotomy. In this lecture we present a proof that this dichotomy is also present in the case of once reinforced random walk, in which the walker's transition probabilities depend upon which edges have previously been traversed by the walker. Afterwards, we discuss the current state of affairs as to which of these two possibilities occurs for specific graphs.