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Quantum Unique Ergodicity for Cayley Graphs of Quasirandom Groups
A finite group G is called C-quasirandom (by Gowers) if all non-trivial irreducible complex representations of G have dimension at least C. For any unit [Formula: see text] function on a finite group we associate the quantum probability measure on the group given by the absolute value squared of the...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Springer Berlin Heidelberg
2023
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10439862/ https://www.ncbi.nlm.nih.gov/pubmed/37605771 http://dx.doi.org/10.1007/s00220-023-04801-x |
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author | Magee, Michael Thomas, Joe Zhao, Yufei |
author_facet | Magee, Michael Thomas, Joe Zhao, Yufei |
author_sort | Magee, Michael |
collection | PubMed |
description | A finite group G is called C-quasirandom (by Gowers) if all non-trivial irreducible complex representations of G have dimension at least C. For any unit [Formula: see text] function on a finite group we associate the quantum probability measure on the group given by the absolute value squared of the function. We show that if a group is highly quasirandom, in the above sense, then any Cayley graph of this group has an orthonormal eigenbasis of the adjacency operator such that the quantum probability measures of the eigenfunctions put close to the correct proportion of their mass on suitably selected subsets of the group that are not too small. |
format | Online Article Text |
id | pubmed-10439862 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-104398622023-08-21 Quantum Unique Ergodicity for Cayley Graphs of Quasirandom Groups Magee, Michael Thomas, Joe Zhao, Yufei Commun Math Phys Article A finite group G is called C-quasirandom (by Gowers) if all non-trivial irreducible complex representations of G have dimension at least C. For any unit [Formula: see text] function on a finite group we associate the quantum probability measure on the group given by the absolute value squared of the function. We show that if a group is highly quasirandom, in the above sense, then any Cayley graph of this group has an orthonormal eigenbasis of the adjacency operator such that the quantum probability measures of the eigenfunctions put close to the correct proportion of their mass on suitably selected subsets of the group that are not too small. Springer Berlin Heidelberg 2023-07-31 2023 /pmc/articles/PMC10439862/ /pubmed/37605771 http://dx.doi.org/10.1007/s00220-023-04801-x Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Magee, Michael Thomas, Joe Zhao, Yufei Quantum Unique Ergodicity for Cayley Graphs of Quasirandom Groups |
title | Quantum Unique Ergodicity for Cayley Graphs of Quasirandom Groups |
title_full | Quantum Unique Ergodicity for Cayley Graphs of Quasirandom Groups |
title_fullStr | Quantum Unique Ergodicity for Cayley Graphs of Quasirandom Groups |
title_full_unstemmed | Quantum Unique Ergodicity for Cayley Graphs of Quasirandom Groups |
title_short | Quantum Unique Ergodicity for Cayley Graphs of Quasirandom Groups |
title_sort | quantum unique ergodicity for cayley graphs of quasirandom groups |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10439862/ https://www.ncbi.nlm.nih.gov/pubmed/37605771 http://dx.doi.org/10.1007/s00220-023-04801-x |
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