Vertex-reinforced random walk is a random process which visits a site with probability proportional to the weight w_k of the number k of previous visits. We show that if w_kâˆ¼k^Î±, then there is a large time T such that after T the walk visits 2, 5, or âˆž sites when Î±1, respectively. More general results are also proven.
|Translated title of the contribution||Phase transition in vertex-reinforced random walks on Z with non-linear reinforecment|
|Pages (from-to)||691 - 700|
|Number of pages||10|
|Journal||Journal of Theoretical Probability|
|Publication status||Published - Dec 2006|