Random paths with bounded local time
Probability
2010-04-22 v3 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.0805.3326,
title = {Random paths with bounded local time},
author = {Itai Benjamini and Nathanael Berestycki},
journal= {arXiv preprint arXiv:0805.3326},
year = {2010}
}
Comments
Title changed; several typos corrected. To appear in Journal of European Mathematical Society.