Shape transition under excess self-intersections for transient random walk

Amine Asselah

Annales de l'I.H.P. Probabilités et statistiques (2010)

  • Volume: 46, Issue: 1, page 250-278
  • ISSN: 0246-0203

Abstract

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We reveal a shape transition for a transient simple random walk forced to realize an excess q-norm of the local times, as the parameter q crosses the value qc(d)=d/(d−2). Also, as an application of our approach, we establish a central limit theorem for the q-norm of the local times in dimension 4 or more.

How to cite

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Asselah, Amine. "Shape transition under excess self-intersections for transient random walk." Annales de l'I.H.P. Probabilités et statistiques 46.1 (2010): 250-278. <http://eudml.org/doc/240710>.

@article{Asselah2010,
abstract = {We reveal a shape transition for a transient simple random walk forced to realize an excess q-norm of the local times, as the parameter q crosses the value qc(d)=d/(d−2). Also, as an application of our approach, we establish a central limit theorem for the q-norm of the local times in dimension 4 or more.},
author = {Asselah, Amine},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {self-intersection local times; large deviations; random walk; random environment; self-intersection local time; large deviation; two-fold intersection; transient random walk; shape transition},
language = {eng},
number = {1},
pages = {250-278},
publisher = {Gauthier-Villars},
title = {Shape transition under excess self-intersections for transient random walk},
url = {http://eudml.org/doc/240710},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Asselah, Amine
TI - Shape transition under excess self-intersections for transient random walk
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2010
PB - Gauthier-Villars
VL - 46
IS - 1
SP - 250
EP - 278
AB - We reveal a shape transition for a transient simple random walk forced to realize an excess q-norm of the local times, as the parameter q crosses the value qc(d)=d/(d−2). Also, as an application of our approach, we establish a central limit theorem for the q-norm of the local times in dimension 4 or more.
LA - eng
KW - self-intersection local times; large deviations; random walk; random environment; self-intersection local time; large deviation; two-fold intersection; transient random walk; shape transition
UR - http://eudml.org/doc/240710
ER -

References

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