Thermalisation for Wigner matrices
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Date
2022-04-15
Publication Type
Journal Article
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yes
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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.
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published
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Journal / series
Volume
282 (8)
Pages / Article No.
109394
Publisher
Elsevier
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Subject
Global law; Local law; Non-crossing partitions; Asymptotic freeness
Organisational unit
02889 - ETH Institut für Theoretische Studien / ETH Institute for Theoretical Studies