Open access
Date
2022-04-15Type
- Journal Article
Abstract
We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem [36] from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to eitW for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000530951Publication status
publishedExternal links
Journal / series
Journal of Functional AnalysisVolume
Pages / Article No.
Publisher
ElsevierSubject
Global law; Local law; Non-crossing partitions; Asymptotic freenessOrganisational unit
02889 - ETH Institut für Theoretische Studien / ETH Institute for Theoretical Studies02889 - ETH Institut für Theoretische Studien / ETH Institute for Theoretical Studies
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