2008/05/21 by Itai Benjamini, Itaï Benjamini, Nathanaël Berestycki +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60G17 #60J65 #60K37 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories #math-ph #math.MP #math.PR #msc:60G17 #msc:60J65 #msc:60K37
paper · pdf · doi:10.48550/arxiv.0805.3326
Title changed; several typos corrected. To appear in Journal of European Mathematical Society.
openalex publication_date 2008/05/21 · arxiv created 2010/04/21 · arxiv updated 2010/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.