Random Walks in Attractive Potentials: The Case of Critical Drifts

Dmitry Ioffe[1]; Yvan Velenik[1]

  • [1] Technion and Université de Genève

Actes des rencontres du CIRM (2010)

  • Volume: 2, Issue: 1, page 11-13
  • ISSN: 2105-0597

Abstract

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We consider random walks in attractive potentials - sub-additive functions of their local times. An application of a drift to such random walks leads to a phase transition: If the drift is small than the walk is still sub-ballistic, whereas the walk is ballistic if the drift is strong enough. The set of sub-critical drifts is convex with non-empty interior and can be described in terms of Lyapunov exponents (Sznitman, Zerner ). Recently it was shown that super-critical drifts lead to a limiting speed. We shall explain that in dimensions d ≥ 2 the transition is always of the first order. (Joint work with Y.Velenik)

How to cite

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Ioffe, Dmitry, and Velenik, Yvan. "Random Walks in Attractive Potentials: The Case of Critical Drifts." Actes des rencontres du CIRM 2.1 (2010): 11-13. <http://eudml.org/doc/115842>.

@article{Ioffe2010,
abstract = {We consider random walks in attractive potentials - sub-additive functions of their local times. An application of a drift to such random walks leads to a phase transition: If the drift is small than the walk is still sub-ballistic, whereas the walk is ballistic if the drift is strong enough. The set of sub-critical drifts is convex with non-empty interior and can be described in terms of Lyapunov exponents (Sznitman, Zerner ). Recently it was shown that super-critical drifts lead to a limiting speed. We shall explain that in dimensions $d\ge 2$ the transition is always of the first order. (Joint work with Y.Velenik)},
affiliation = {Technion and Université de Genève; Technion and Université de Genève},
author = {Ioffe, Dmitry, Velenik, Yvan},
journal = {Actes des rencontres du CIRM},
keywords = {self-attractive polymer; ballisticity; random walk; phase transition},
language = {eng},
month = {12},
number = {1},
pages = {11-13},
publisher = {CIRM},
title = {Random Walks in Attractive Potentials: The Case of Critical Drifts},
url = {http://eudml.org/doc/115842},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Ioffe, Dmitry
AU - Velenik, Yvan
TI - Random Walks in Attractive Potentials: The Case of Critical Drifts
JO - Actes des rencontres du CIRM
DA - 2010/12//
PB - CIRM
VL - 2
IS - 1
SP - 11
EP - 13
AB - We consider random walks in attractive potentials - sub-additive functions of their local times. An application of a drift to such random walks leads to a phase transition: If the drift is small than the walk is still sub-ballistic, whereas the walk is ballistic if the drift is strong enough. The set of sub-critical drifts is convex with non-empty interior and can be described in terms of Lyapunov exponents (Sznitman, Zerner ). Recently it was shown that super-critical drifts lead to a limiting speed. We shall explain that in dimensions $d\ge 2$ the transition is always of the first order. (Joint work with Y.Velenik)
LA - eng
KW - self-attractive polymer; ballisticity; random walk; phase transition
UR - http://eudml.org/doc/115842
ER -

References

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  1. Dmitry Ioffe and Yvan Velenik. Ballistic phase of self-interacting random walks. In Analysis and stochastics of growth processes and interface models, pages 55–79. Oxford Univ. Press, Oxford, 2008. Zbl1255.60168MR2603219
  2. Martin P. W. Zerner. Directional decay of the Green’s function for a random nonnegative potential on Z d . Ann. Appl. Probab., 8(1):246–280, 1998. Zbl0938.60098MR1620370

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