In this talk, I will consider the noise sensitivity of dynamical critical planer continuum percolation models, such as the Boolean model and Voronoi percolation model. While similar results for the Voronoi percolation have previously been shown in Vanneuville (2021) under the so-called frozen dynamics, we instead consider the Ornstein-Uhlenbeck (OU) dynamics.

A critical planer dynamical percolation model is said to be noise sensitive if the ±1-indicator of a left-right occupied crossing of large squares of side length L in the model is sensitive to small noises in the underlying system. We introduce the noise according to the OU dynamics and show a sharp transition result : when the amount of noise tends to zero as L → ∞ fast enough, then the model is not sensitive to the noise, while if it doesn't tend to zero fast enough, the model becomes noise sensitive. The main tool is a notion of spectral point process based on the chaos expansion of the crossing functionals, which parallels the corresponding notion of spectral samples in the discrete setting.

The talk is based of a joint work with Giovanni Peccati and Yogeshwaran Dhandapani