Geodesic
Random paths with bounded local time
Journal of the European Mathematical Society, Tome 12 (2010) no. 4, pp. 819-854 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/216
Classification : 60-XX, 00-XX
Keywords: Brownian motion, local times, self-repelling processes, Ray-Knight theorem, entropic repulsion 
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     author = {Itai Benjamini and Nathana\"el Berestycki},
     title = {Random paths with bounded local time},
     journal = {Journal of the European Mathematical Society},
     pages = {819--854},
     year = {2010},
     volume = {12},
     number = {4},
     doi = {10.4171/jems/216},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/216/}
}
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Itai Benjamini; Nathanaël Berestycki. Random paths with bounded local time. Journal of the European Mathematical Society, Tome 12 (2010) no. 4, pp. 819-854. doi: 10.4171/jems/216

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