Exclusion sensitivity of Boolean functions
Journal article, 2013

Recently the study of noise sensitivity and noise stability of Boolean functions has received considerable attention. The purpose of this paper is to extend these notions in a natural way to a different class of perturbations, namely those arising from running the symmetric exclusion process for a short amount of time. In this study, the case of monotone Boolean functions will turn out to be of particular interest. We show that for this class of functions, ordinary noise sensitivity and noise sensitivity with respect to the complete graph exclusion process are equivalent. We also show this equivalence with respect to stability. After obtaining these fairly general results, we study “exclusion sensitivity” of critical percolation in more detail with respect to medium-range dynamics. The exclusion dynamics, due to its conservative nature, is in some sense more physical than the classical i.i.d. dynamics. Interestingly, we will see that in order to obtain a precise understanding of the exclusion sensitivity of percolation, we will need to describe how typical spectral sets of percolation diffuse under the underlying exclusion process.

noise sensitivity

Exclusion sensitivity

Noise sensitivity

critical percolation


Erik Broman

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg

C. Garban

École Normale Supérieure de Lyon

Jeffrey Steif

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Probability Theory and Related Fields

0178-8051 (ISSN) 1432-2064 (eISSN)

Vol. 155 3-4 621-663

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