Self-Attractive Random Walks: The Case of Critical Drifts

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.

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

References in corpus (3)

• Large deviations for random walks under subexponentiality: the big-jump domain
• The Statistical Mechanics of Stretched Polymers
• Crossing velocities for an annealed random walk in a random potential

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• Ornstein-Zernike behavior for Ising models with infinite-range interactions