Thermalisation for Wigner matrices Cipolloni, Giorgio ; https://orcid.org/0000-0002-4901-7992 Erdös, László ; https://orcid.org/0000-0001-5366-9603 Schröder, Dominik J ; https://orcid.org/0000-0002-2904-1856 ddc:500 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 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. Elsevier 2022 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/10732 https://research-explorer.ista.ac.at/download/10732/11690 Cipolloni G, Erdös L, Schröder DJ. Thermalisation for Wigner matrices. <i>Journal of Functional Analysis</i>. 2022;282(8). doi:<a href="https://doi.org/10.1016/j.jfa.2022.109394">10.1016/j.jfa.2022.109394</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2022.109394 info:eu-repo/semantics/altIdentifier/issn/0022-1236 info:eu-repo/semantics/altIdentifier/e-issn/1096-0783 info:eu-repo/semantics/altIdentifier/wos/000781239100004 info:eu-repo/semantics/altIdentifier/arxiv/2102.09975 info:eu-repo/semantics/openAccess