Brownian Entropic Repulsion

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 4.5860... as high as required by the conditioning (the exact value of this constant involves the first zero of a Bessel function). I will also describe other conditionings of Brownian motion in which this principle of entropic repulsion manifests itself.

Joint work with Itai Benjamini.