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Self-Attractive Random Walks: The Case of Critical Drifts

Ioffe, Dmitry
Published in Communications in Mathematical Physics. 2012, vol. 313, p. 209-235
Abstract 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.
Keywords Self-attractive random walksSelf-attractive polymersStrecthed polymersCritical driftLLNCLTPhase transition
arXiv: 1104.4615
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IOFFE, Dmitry, VELENIK, Yvan Alain. Self-Attractive Random Walks: The Case of Critical Drifts. In: Communications in Mathematical Physics, 2012, vol. 313, p. 209-235. https://archive-ouverte.unige.ch/unige:15716

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Deposited on : 2011-05-05

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