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Probability Seminars

Metrics and random walks on 2D critical percolation and CLE

With Yizheng Yuan

Metrics and random walks on 2D critical percolation and CLE

Intrinsic metrics (a.k.a. chemical distance) and random walks on percolation models have been attracting a lot of mathematical attention. The case of (low-dimensional) critical percolation, however, has remained poorly understood. In this talk, I will explain how to construct the scaling limits of the intrinsic metric and the random walk on 2D critical percolation clusters. More generally, for each CLE _kappa, kappa in ]4,8[, we construct the canonical shortest-path metric and diffusion process on its gasket. We show that the metrics are uniquely characterised by their Markovian property, and that they are scale-covariant and conformally covariant.

This talk is based on joint works with Valeria Ambrosio, Irina Đanković, Maarten Markering, and Jason Miller.

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