Self-Attractive Random Walks: The Case of Critical Drifts

Details Self-Attractive Random Walks: The Case of Critical Drifts Self-Attractive Random Walks: The Case of Critical Drifts

2011-04-24

arxiv.org/abs/1104.4615v4

Mathematics

Probability

Final version sent to the publisher. To appear in Communications in Mathematical Physics

Scientific paper

Self-attractive random walks undergo a phase transition in terms of the applied drift: If the drift is strong enough, then the walk is ballistic, whereas in the case of small drifts self-attraction wins and the walk is sub-ballistic. We show that, in any dimension at least 2, this transition is of first order. In fact, we prove that the walk is already ballistic at critical drifts, and establish the corresponding LLN and CLT.

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