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Quantum Unique Ergodicity for Cayley graphs of quasirandom groups

Magee, Michael; Thomas, Joe; Zhao, Yufei

Authors

Dr Joe Thomas joe.thomas@durham.ac.uk
Post Doctoral Research Associate

Yufei Zhao



Abstract

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 ℓ2 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.

Citation

Magee, M., Thomas, J., & Zhao, Y. (2023). Quantum Unique Ergodicity for Cayley graphs of quasirandom groups. Communications in Mathematical Physics, https://doi.org/10.1007/s00220-023-04801-x

Journal Article Type Article
Acceptance Date Jun 15, 2023
Online Publication Date Aug 31, 2023
Publication Date 2023
Deposit Date Jul 19, 2023
Publicly Available Date Sep 1, 2024
Journal Communications in Mathematical Physics
Print ISSN 0010-3616
Electronic ISSN 1432-0916
Publisher Springer
Peer Reviewed Peer Reviewed
DOI https://doi.org/10.1007/s00220-023-04801-x
Public URL https://durham-repository.worktribe.com/output/1168252
Publisher URL https://doi.org/10.1007/s00220-023-04801-x

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