Random paths with bounded local time

Itai Benjamini; Nathanaël Berestycki

Journal of the European Mathematical Society (2010)

  • Volume: 012, Issue: 4, page 819-854
  • ISSN: 1435-9855

Abstract

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We consider one-dimensional Brownian motion conditioned (in a suitable sense) to have a local time at every point and at every moment bounded by some fixed constant. Our main result shows that a phenomenon of entropic repulsion occurs: that is, this process is ballistic and has an asymptotic velocity approximately 4.58... as high as required by the conditioning (the exact value of this constant involves the first zero of a Bessel function). We also study the random walk case and show that the process is asymptotically ballistic but with an unknown speed.

How to cite

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Benjamini, Itai, and Berestycki, Nathanaël. "Random paths with bounded local time." Journal of the European Mathematical Society 012.4 (2010): 819-854. <http://eudml.org/doc/277221>.

@article{Benjamini2010,
abstract = {We consider one-dimensional Brownian motion conditioned (in a suitable sense) to have a local time at every point and at every moment bounded by some fixed constant. Our main result shows that a phenomenon of entropic repulsion occurs: that is, this process is ballistic and has an asymptotic velocity approximately 4.58... as high as required by the conditioning (the exact value of this constant involves the first zero of a Bessel function). We also study the random walk case and show that the process is asymptotically ballistic but with an unknown speed.},
author = {Benjamini, Itai, Berestycki, Nathanaël},
journal = {Journal of the European Mathematical Society},
keywords = {Brownian motion; local times; self-repelling processes; Ray-Knight theorem; entropic repulsion; Brownian motion; local times; self-repelling processes; Ray-Knight theorem; entropic repulsion},
language = {eng},
number = {4},
pages = {819-854},
publisher = {European Mathematical Society Publishing House},
title = {Random paths with bounded local time},
url = {http://eudml.org/doc/277221},
volume = {012},
year = {2010},
}

TY - JOUR
AU - Benjamini, Itai
AU - Berestycki, Nathanaël
TI - Random paths with bounded local time
JO - Journal of the European Mathematical Society
PY - 2010
PB - European Mathematical Society Publishing House
VL - 012
IS - 4
SP - 819
EP - 854
AB - We consider one-dimensional Brownian motion conditioned (in a suitable sense) to have a local time at every point and at every moment bounded by some fixed constant. Our main result shows that a phenomenon of entropic repulsion occurs: that is, this process is ballistic and has an asymptotic velocity approximately 4.58... as high as required by the conditioning (the exact value of this constant involves the first zero of a Bessel function). We also study the random walk case and show that the process is asymptotically ballistic but with an unknown speed.
LA - eng
KW - Brownian motion; local times; self-repelling processes; Ray-Knight theorem; entropic repulsion; Brownian motion; local times; self-repelling processes; Ray-Knight theorem; entropic repulsion
UR - http://eudml.org/doc/277221
ER -

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