ICTS:31843

Video URL

Noise stability and sensitivity in continuum percolation

Noise stability and sensitivity in continuum percolation

(2025). Noise stability and sensitivity in continuum percolation. SciVideos. https://youtu.be/gdApzIlyIp4

Noise stability and sensitivity in continuum percolation. SciVideos, May. 15, 2025, https://youtu.be/gdApzIlyIp4 

          @misc{ scivideos_ICTS:31843,
            doi = {},
            url = {https://youtu.be/gdApzIlyIp4},
            author = {},
            keywords = {},
            language = {en},
            title = { Noise stability and sensitivity in continuum percolation},
            publisher = {},
            year = {2025},
            month = {may},
            note = {ICTS:31843 see, \url{https://scivideos.org/index.php/icts-tifr/31843}}
          }
Yogeshwaran D
Talk numberICTS:31843
Source RepositoryICTS-TIFR

Abstract

We look at the stability and sensitivity of planar percolation models generated by a Poisson point process under re-sampling dynamics. Noise stability refers to whether certain global percolation events remain unchanged when a small fraction of points are re-sampled, while noise sensitivity means these events become nearly independent even when only arbitrarily small fraction of points are re-sampled.

To analyze these properties, one wants to estimate chaos coefficients in the Wiener-Itô chaos expansion for Poisson functionals, analogue of Fourier-Walsh expansion for functionals of random bits. Motivated by substantial progress in the case of random bits, we introduce two tools to estimate the chaos coefficients. First approach is via stopping sets, which serve as a continuum analogue of randomized algorithms, and the second approach is using pivotal and spectral samples, which provide sharper bounds.

We illustrate these methods using two well-known models: Poisson Boolean percolation, where unit balls are placed at Poisson points, and Voronoi percolation, where Voronoi cells based on Poisson points are randomly retained. Our focus will be on sharp noise sensitivity or stability of crossing events, specifically whether a large rectangle is traversed by a connected component of the percolation model.

The talk is based on joint projects with Chinmoy Bhattacharjee, Guenter Last, and Giovanni Peccati