Abstract
This paper establishes a dimension-independent upper bound on the maximal correlation between Boolean functions of dependent random variables, in terms of the second and third singular values in their spectral decomposition, and the anti-concentration properties of the second singular vectors. This result has notable consequences, among which are: A strengthening of Witsenhausen's lower bound on the probability of disagreement between Boolean functions; a Poincaré inequality for bounded-cardinality functions; and improved lower bounds on the isoperimetric constant of Markov chains.
Original language | English |
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Title of host publication | 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Pages | 1284-1289 |
Number of pages | 6 |
ISBN (Electronic) | 9781538682098 |
DOIs | |
State | Published - 12 Jul 2021 |
Event | 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia Duration: 12 Jul 2021 → 20 Jul 2021 |
Publication series
Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2021-July |
ISSN (Print) | 2157-8095 |
Conference
Conference | 2021 IEEE International Symposium on Information Theory, ISIT 2021 |
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Country/Territory | Australia |
City | Virtual, Melbourne |
Period | 12/07/21 → 20/07/21 |
Bibliographical note
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