# 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

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topBenjamini, 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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