One-arm probability for the metric Gaussian free field in low dimensions

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• Pierre-Francois Rodriguez (Imperial College London)
• Wednesday 10 July 2024, 10:15-11:15
• Seminar Room 1, Newton Institute.

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SSDW01 - Self-interacting processes

The study of percolation for the excursion sets of the Gaussian free field on transient weighted graphs was first considered by Lebowitz-Saleur/Lebowitz-Bricmont-Maes in the mid 80’s, and more recently re-instigated by R.-Sznitman (‘12). Following an idea of Lupu (‘16), we investigate a variant of this percolation model, obtained by considering the  excursion sets of the free field on the corresponding metric graph. We will discuss the behavior of the probability to connect a point to large distances (the so-called “one-arm” probability) for the metric-graph version in low transient dimensions. A case in point is the usual Euclidean lattice in dimension three. Based on joint works with A. Drewitz (Köln) and A. Prévost (Genève).

This talk is part of the Isaac Newton Institute Seminar Series series.

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