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On the number and size of holes in the growing ball of first-passage percolation
[article]
2022
arXiv
pre-print
First-passage percolation is a random growth model defined on ℤ^d using i.i.d. nonnegative weights (τ_e) on the edges. Letting T(x,y) be the distance between vertices x and y induced by the weights, we study the random ball of radius t centered at the origin, B(t) = {x ∈ℤ^d : T(0,x) ≤ t}. It is known that for all such τ_e, the number of vertices (volume) of B(t) is at least order t^d, and under mild conditions on τ_e, this volume grows like a deterministic constant times t^d. Defining a hole in
arXiv:2205.09733v1
fatcat:jhob6t5izbcqllfjdkxrj25ihe