Exclusion Sensitivity of Boolean Functions
Preprint, 2011

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 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

influences

Probability

Fourier analysis

Författare

Erik Broman

Chalmers, Matematiska vetenskaper

Göteborgs universitet

Christophe Garban

Jeffrey Steif

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Ämneskategorier

Matematik

Annan matematik

Fundament

Grundläggande vetenskaper