article published yes Giorgio Cipolloni author 42198EFA-F248-11E8-B48F-1D18A9856A870000-0002-4901-7992 László Erdös author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603 Dominik J Schröder author 408ED176-F248-11E8-B48F-1D18A9856A870000-0002-2904-1856 LaEr department 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. https://research-explorer.ista.ac.at/download/10732/11690/2022_JourFunctionalAnalysis_Cipolloni.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Elsevier2022 eng 0022-1236 1096-0783 2102.09975 00078123910000410.1016/j.jfa.2022.109394 2828 G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022). G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,” <i>Journal of Functional Analysis</i>, vol. 282, no. 8. Elsevier, 2022. 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> Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394. Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation for Wigner Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2022. <a href="https://doi.org/10.1016/j.jfa.2022.109394">https://doi.org/10.1016/j.jfa.2022.109394</a>. Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Thermalisation for Wigner matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href="https://doi.org/10.1016/j.jfa.2022.109394">https://doi.org/10.1016/j.jfa.2022.109394</a> Cipolloni, Giorgio, et al. “Thermalisation for Wigner Matrices.” <i>Journal of Functional Analysis</i>, vol. 282, no. 8, 109394, Elsevier, 2022, doi:<a href="https://doi.org/10.1016/j.jfa.2022.109394">10.1016/j.jfa.2022.109394</a>. 107322022-02-06T23:01:30Z2024-10-09T21:01:33Z