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math.PR2018★ 1 cited
Ergodicity of the number of infinite geodesics originating from zero
Shuta Nakajima
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…
math.PR2018
Divergence of non-random fluctuation in First Passage Percolation
Shuta Nakajima
We study non-random fluctuation in the first passage percolation on and show that it diverges for any dimension. We also prove the divergence of the non-random shape…