## 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_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 |
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Original language | English |

Pages (from-to) | 691 - 700 |

Number of pages | 10 |

Journal | Journal of Theoretical Probability |

Volume | 19 |

Publication status | Published - Dec 2006 |