Abstract
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_k∼k^α, then there is a large time T such that after T the walk visits 2, 5, or ∞ sites when α1, 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 |
|---|---|
| Original language | English |
| Pages (from-to) | 691 - 700 |
| Number of pages | 10 |
| Journal | Journal of Theoretical Probability |
| Volume | 19 |
| Publication status | Published - Dec 2006 |
Bibliographical note
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