Fast convergence to an invariant measure for non-intersecting 3-dimensional Brownian paths

2010/08/28 by Gregory F. Lawler, Lawler, Gregory F., Brigitta Vermesi +1 · 1 citation
Mathematics · #60J65 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60J65

paper · pdf · doi:10.48550/arxiv.1008.4830

v2: changes in notation

openalex publication_date 2010/08/28 · arxiv created 2012/11/29 · arxiv updated 2012/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider pairs of 3-dimensional Brownian paths, started at the origin and conditioned to have no intersections after time zero. We show that there exists a unique measure on pairs of paths that is invariant under this conditioning, while improving the previously known rate of convergence to stationarity.

Citations

• Intersection exponents for biased random walks on discrete cylinders

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