arXiv subjects

Malin Palö Forsström

Publications and source records attributed to Malin Palö Forsström.

20 records · Page 2Linked to original sources

arXiv2015

A Noise Sensitivity Theorem for Schreier Graphs

During the past 15 years, several extensions of the concept of noise sensitivity first coined in~\cite{schramm2000}, has been studied. One such extension was studied in ??, where the definition of noise sensitivity was extended to noise corresponding to any sequence of irreducible and reversible Markov chains. In this paper we focus on the case where the Markov chain is a random walk on a Schreier graph, and show that the Benjamini-Kalai-Schramm theorem, connecting influences to noise sensitivity, holds in this setting. We then apply this result to give an alternative proof of one of the main results from a recent paper on exclusion sensitivity by Broman, Garban and Steif.

math.PR↗

arXiv2015

Noise Sensitivity and Noise Stability for Markov Chains: Existence Results

During the past 15 years, several extensions of the concepts noise sensitivity and noise stability, first coined in~\cite{schramm2000}, has been studied. The purpose in this paper is to give definitions of this concepts in the setting of continuous time Markov chains, which then unifies many of the previously considered generalizations. In addition, a considerable amount of time is spent on proving the existence of sequences of noise stable and nondegenerate functions with respect to various classes of Markov chains, a problem which interestingly will appear to have close connections to the so called localization of eigenvectors, a problem which in the setting of random graphs has recently been given a lot of attention.

math.PR↗