Quantum Unique Ergodicity for Cayley Graphs of Quasirandom Groups
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220_2023_Article_4801.pdf
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Author(s)
Magee, Michael
Thomas, Joe
Zhao, Yufei
Date Issued
July 31, 2023
Publisher
Springer Berlin Heidelberg
Citation
Magee, Michael, Thomas, Joe and Zhao, Yufei. 2023. "Quantum Unique Ergodicity for Cayley Graphs of Quasirandom Groups."
Version
Final published version
Abstract
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
$$\ell ^{2}$$
ℓ
2
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International license
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DOI of Published Version
https://doi.org/10.1007/s00220-023-04801-x
