Pré-Publication, Document De Travail Année : 2024

Disjoint finite geodesics in first-passage percolation

Olivier Durieu
Jean-Baptiste Gouéré
Antonin Jacquet
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Résumé

We investigate first-passage percolation on the lattice Zd for dimensions d2. Each edge e of the graph is assigned an independent copy of a non-negative random variable τ. We only assume P[τ=0]<pc(Zd), the critical probability threshold for Bernoulli bond percolation on Zd. We obtain lower bounds of order nαd (where αd>0 is explicit) for the probability of having two disjoint geodesics between two pairs of neighbouring vertices at distance n. Additionally, under more specific assumptions on the distribution of τ, we obtain similar lower bounds for the probability of having two disjoint geodesics (except for their starting and ending points) between the same two vertices.
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Dates et versions

hal-04661565 , version 1 (24-07-2024)

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Olivier Durieu, Jean-Baptiste Gouéré, Antonin Jacquet. Disjoint finite geodesics in first-passage percolation. 2024. ⟨hal-04661565⟩
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