Ergodicity of the number of infinite geodesics originating from zero

2018/07/16 by Nakajima, Shuta
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1807.05900

Abstract

First-passage percolation is a random growth model which has a metric structure. An infinite geodesic is an infinite sequence whose all sub-sequences are shortest paths. One of the important quantity is the number of infinite geodesics originating from the origin. When d=2 and an edge distribution is continuous, it is proved to be almost surely constant [D. Ahlberg, C. Hoffman. Random coalescing geodesics in first-passage percolation]. In this paper, we will prove the same result for higher dimensions and general distributions.

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