談話会

数理科学科談話会 (2018/11/22)

2018.11.12 Mon up
<<談話会>>
日時: 2018年11月22日(木) 18:00~19:00
場所: 立命館大学びわこ・くさつキャンパス(BKC)
      ウェストウィング6階談話会室
タイトル:On the spectrum of non-commuting polynomials in random permutation matrices

講演者: Benoît Collins (京都大学・数学教室)

アブストラクト:
To any non-commuting polynomial P in k non-commuting unitaries and its inverses we can associate an n x n random matrix obtained by replacing the unitaries by k iid random uniform permutation matrices. In case P is self-adjoint, free probability predicts the histogram of eigenvalues of the associated random matrix when n is large, by supplying a limiting probability distribution. We are interested in the problem of whether there can be eigenvalues far away from the support of the limiting distribution. Our main result is that there is at most one such eigenvalue which we will describe. As a corollary, we are able to prove the so-called Alon’s generalized second eigenvalue conjecture. Time allowing, we will describe this conjecture and new techniques used to prove our main result. This talk is based on joint work with Charles Bordenave.

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