Chinmoy Bhattacharjee, Univ. Hamburg: Spectra of Poisson Functionals and Applications in Continuum Percolation (Oberseminar Mathematische Stochastik)
Wednesday, 17.04.2024 16:30 im Raum SRZ 203
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 \to\infty 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 Yogesh-
waran Dhandapani.
Angelegt am 25.01.2024 von Anita Kollwitz
Geändert am 15.04.2024 von Anita Kollwitz
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