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• W3103237002 abstract "Consider a finite sequence of independent random permutations, chosen uniformly either among all permutations or among all matchings on n points. We show that, in probability, as n goes to infinity, these permutations viewed as operators on the (n-1) dimensional vector space orthogonal to the vector with all coordinates equal to 1, are asymptotically strongly free. Our proof relies on the development of a matrix version of the non-backtracking operator theory and a refined trace method. As a byproduct, we show that the non-trivial eigenvalues of random n-lifts of a fixed based graphs approximately achieve the Alon-Boppana bound with high probability in the large n limit. This result generalizes Friedman's Theorem stating that with high probability, the Schreier graph generated by a finite number of independent random permutations is close to Ramanujan. Finally, we extend our results to tensor products of random permutation matrices. This extension is especially relevant in the context of quantum expanders." @default.
• W3103237002 created "2020-11-23" @default.
• W3103237002 creator A5000758322 @default.
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• W3103237002 date "2019-11-01" @default.
• W3103237002 modified "2023-10-11" @default.
• W3103237002 title "Eigenvalues of random lifts and polynomials of random permutation matrices" @default.
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• W3103237002 doi "https://doi.org/10.4007/annals.2019.190.3.3" @default.
• W3103237002 hasPublicationYear "2019" @default.
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