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Scientific article
English

Self-Attractive Random Walks: The Case of Critical Drifts

Published inCommunications in Mathematical Physics, vol. 313, p. 209-235
Collection
  • Open Access - Licence nationale Springer
Publication date2012
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 walks
  • Self-attractive polymers
  • Strecthed polymers
  • Critical drift
  • LLN
  • CLT
  • Phase transition
Classification
  • arxiv : math.PR
Citation (ISO format)
IOFFE, Dmitry, VELENIK, Yvan. Self-Attractive Random Walks: The Case of Critical Drifts. In: Communications in Mathematical Physics, 2012, vol. 313, p. 209–235. doi: 10.1007/s00220-012-1492-1
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Identifiers
ISSN of the journal1432-0916
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