Self-Attractive Random Walks: The Case of Critical Drifts

• DOI: 10.1007/s00220-012-1492-1
• Publication Date: 2012-05-16T10:32:40Z
• Authors: Dmitry Ioffe; Yvan Velenik
• Keywords: Self-attractive random walks; Strecthed polymers; LLN; Statistical Mechanics (cond-mat.stat-mech); CLT; Probability (math.PR); Self-attractive polymers; FOS: Physical sciences; Mathematical Physics (math-ph); FOS: Mathematics; ddc:510; info:eu-repo/classification/ddc/510; Critical drift; Mathematics - Probability; Condensed Matter - Statistical Mechanics; Mathematical Physics; Phase transition

Final version sent to the publisher. To appear in Communications in Mathematical Physics<br/>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.<br/>