@inproceedings{f3b3214796f14460ae61d5496ef4ab30,
title = "Expander Random Walks: The General Case and Limitations",
abstract = "Cohen, Peri and Ta-Shma [11] considered the following question: Assume the vertices of an expander graph are labelled by ±1. What “test” functions f : {±1}t → {±1} can or cannot distinguish t independent samples from those obtained by a random walk? [11] considered only balanced labellings, and proved that for all symmetric functions the distinguishability goes down to zero with the spectral gap λ of the expander G. In addition, [11] show that functions computable by AC0 circuits are fooled by expanders with vanishing spectral expansion. We continue the study of this question. We generalize the result to all labelling, not merely balanced ones. We also improve the upper bound on the error of symmetric functions. More importantly, we give a matching lower bound and show a symmetric function with distinguishability going down to zero with λ but not with t.",
keywords = "Expander Graphs, Lower Bounds, Random Walks",
author = "Gil Cohen and Dor Minzer and Shir Peleg and Aaron Potechin and Amnon Ta-Shma",
note = "Publisher Copyright: {\textcopyright} Gil Cohen, Dor Minzer, Shir Peleg, Aaron Potechin, and Amnon Ta-Shma; licensed under Creative Commons License CC-BY 4.0; 49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022 ; Conference date: 04-07-2022 Through 08-07-2022",
year = "2022",
month = jul,
day = "1",
doi = "10.4230/LIPIcs.ICALP.2022.43",
language = "אנגלית",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Mikolaj Bojanczyk and Emanuela Merelli and Woodruff, {David P.}",
booktitle = "49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022",
}