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
Daniel Ahlberg and Mia Deijfen (Stockholm University).