Liberté asymptotique forte pour des permutations aléatoires

Jeudi 7 décembre 14:00-15:00 - Benoît Collins - Université de Kyoto

Résumé : n by n permutation matrices act naturally on the (n − 1)-dimensional vector subspace of C^n of vectors whose components add up to zero. We prove that random independent permutations, viewed as operators on this vector subspace, are asymptotically strongly free with high probability. While this is a counterpart of a previous result by the presenter and Male in the case of a uniform distribution on unitary matrices, the techniques required for random permutations are very different, and rely on the development of a matrix version of the theory of non-backtracking operators. This is joint work with Charles Bordenave.

Lieu : salle 117/119 du bâtiment 425

Liberté asymptotique forte pour des permutations aléatoires  Version PDF