Chaos and concentration in spatial growth models

Sfragara Matteo, Stockholm University

A decade and a half ago Chatterjee established the first rigorous connection between anomalous fluctuations (superconcentration) and a chaotic behaviour of the ground state in certain Gaussian disordered systems. We study the connection between chaos and concentration in spatial growth models, like first-passage percolation (FPP) and last-passage percolation (LPP), and we prove that they exhibit a chaotic behaviour. This extends previous work on the topic, and illustrates that this is a phenomenon that can be expected more widely. The notion of ‘chaos' refers to the sensitivity of the optimal path (geodesic) when exposed to a slight perturbation. In FPP on Z^d the geodesic is the time-minimizing path from the origin to a vertex v, while in LPP on the square lattice [0,n]^2 the geodesic is the weight-maximizing up-right path from (0,0) to (n,n). This talk is based on two joint works with D. Ahlberg and M. Deijfen.

Area: CS37 - Percolation (Matteo Quattropani)

Keywords: chaos, geodesics, first-passage percolation, last-passage percolation

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