Random paths with bounded local time

Details Random paths with bounded local time Random paths with bounded local time

2008-05-21

arxiv.org/abs/0805.3326v3

Mathematics

Probability

Title changed; several typos corrected. To appear in Journal of European Mathematical Society.

Scientific paper

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.

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