Open access
Datum
2022-04-15Typ
- 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. Mehr anzeigen
Persistenter Link
https://doi.org/10.3929/ethz-b-000530951Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
Journal of Functional AnalysisBand
Seiten / Artikelnummer
Verlag
ElsevierThema
Global law; Local law; Non-crossing partitions; Asymptotic freenessOrganisationseinheit
02889 - ETH Institut für Theoretische Studien / ETH Institute for Theoretical Studies02889 - ETH Institut für Theoretische Studien / ETH Institute for Theoretical Studies