The chemical distance in random interlacements in the low-intensity regime

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• Saraí Hernández-Torres (Technion)
• Tuesday 10 May 2022, 14:00-15:00
• MR12.

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Random interlacements is a Poissonian soup of doubly-infinite random walk trajectories on Z^{d, with a parameter u > 0 controlling the intensity of the Poisson point process. In a natural way, the model defines a percolation on the edges of Z}d with long-range correlations. We consider the time constant associated to the chemical distance in random interlacements at low intensity u > 0. It is conjectured that the time constant times u^{1/2} converges to the Euclidean norm, as u ↓ 0. In dimensions d ≥ 5, we prove a sharp upper bound and an almost sharp lower bound for the time constant as the intensity decays to zero. Joint work with Eviatar Procaccia and Ron Rosenthal.

This talk is part of the Probability series.

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