Malo Hillairet

Noise sensitivity of 0-1 valued functions has been introduced by Benjamini, Kalai and Schramm in order to describe decorrelation of percolation crossing events under the effect of a noise. First-passage percolation is a percolation model of which the observables are travel times, also called geodesic lengths. This model has been studied a lot, but seldom from the viewpoint of noise sensitivity. It has been conjectured by Benjamini that the indicator functions of some events related to travel times are noise sensitive, and Ahlberg and de la Riva recently proved it is true for particularly symmetric versions of travel times.

In this talk, we introduce an extended definition of noise sensitivity adapted to functions which may take any real value instead of just 0 and 1, and we generalize the BKS theorem to that framework. We then deduce new results depicting noise sensitive behavior in first-passage percolation for the same travel times as Ahlberg and de la Riva.