Visibility in the vacant set of the Brownian interlacements and the\n Brownian excursion process

2017/09/26 by Olof Elias, Elias, Olof, Johan Tykesson +1 · 1 citation
Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1709.09052

openalex publication_date 2017/09/26 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We consider the Brownian interlacements model in Euclidean space, introduced\nby A.S. Sznitman in citesznitman2013scaling. We give estimates for the\nasymptotics of the visibility in the vacant set. We also consider visibility\ninside the vacant set of the Brownian excursion process in the unit disc and\nshow that it undergoes a phase transition regarding visibility to infinity as\nin citebenjamini2009visibility. Additionally, we determine the critical\nvalue and that there is no visibility to infinity at the critical intensity.\n

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