First Passage Percolation, Local Uniqueness for Interlacements and Capacity of Random Walk

Article Article scientifique Article First Passage Percolation, Local Uniqueness for Interlacements and Capacity of Random Walk eng 2025-01-11 2025-02 author Prevost Alexis 0000-0001-7273-0481 402355 10.1007/s00220-024-05195-0 0010-3616 https://link.springer.com/10.1007/s00220-024-05195-0 <p>The study of first passage percolation (FPP) for the random interlacements model has been initiated in Andres and Prévost (Ann Appl Probab 34(2):1846–1895), where it is shown that on $$\mathbb {Z}^d$$ Z d , $$d\ge 3$$ d ≥ 3 , the FPP distance is comparable to the graph distance with high probability. In this article, we give an asymptotically sharp lower bound on this last probability, which additionally holds on a large class of transient graphs with polynomial volume growth and polynomial decay of the Green function. When considering the interlacement set in the low-intensity regime, the previous bound is in fact valid throughout the near-critical phase. In low dimension, we also present two applications of this FPP result: sharp large deviation bounds on local uniqueness of random interlacements, and on the capacity of a random walk in a ball.</p> Dewey 510 25 Section de mathématiques 11 false Communications in Mathematical Physics 406 2 54b7f71e-12c3-4d4e-b422-b021656fbae5 Article (Published version) Public Article_scientifique_from_crossref.pdf 1779854 application/pdf CC BY-4.0 916771589a13d9ad99ae784c8fba2639b3670a9968718a87f2bc0d070bd80546 openAccess Faculté des sciences / Section de mathématiques

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First Passage Percolation, Local Uniqueness for Interlacements and Capacity of Random Walk	Communications in Mathematical Physics			2025	4	277

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Prevost, Alexis