立命館大学数理科学科

<<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.

• Date: 8 Nov. (Thu.)
• Place: W.W. 6th-floor, Colloquium Room
• Time: 16:30-18:00
• Speaker: Tadashi Ono (University of Tsukuba)
• Title: TBA

• Date: 25 Oct. (Thu.)
• Place: W.W. 6th-floor, Colloquium Room

• Time: 16:30-16:50
• Speaker: Masahiro Kinuya (Ritsumeikan University)
• Title: Euler-Maruyama type approximation of stochastic PDEs by orthogonal random variables

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• ​Time: 16:50-17:10
• Speaker: Yuta Nakamura (Ritsumeikan University)
• Title: Approximation of Heston model by a lattice on 3-dimensional Heisenberg group

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• Time: 17:10-17:30
• Speaker: Yuki Semba (Ritsumeikan University)
• Title: Polya Urn Binomial Model for Option Price

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• Time: 17:30-17:50
• Speaker: Tsuyoshi Kinoshita (Ritsumeikan University)
• Title: Default Contagion with Domino Effect as a Point Process

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• Time: 17:50-18:10
• Speaker: Shuji Tamada (Ritsumeikan University)
• Title: Thermodynamic Approach to Whole-Life Insurance: An Evaluation Method of Surrender Risk

• Date:  27 Sep. (Thu.), 4 Oct. (Thu.) and 11 Oct. (Thu.)
• Place: W.W. 6th-floor, Colloquium Room
• Time: 16:30-18:00
• Speaker: Ying Jiao (Université Claude Bernard Lyon 1)
• Title: CIR models with jumps
• Abstract:

• Date: 20 Sep. (Thu.)
• Place: W.W. 6th-floor, Colloquium Room
• Time: 16:30-18:00
• Speaker: Libo Li (University of New South Wales)
• Title: On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case
• Abstract:

• Date: 13 Sep. (Thu.)
• Place: W.W. 6th-floor, Colloquium Room
• Time: 15:00-18:00
• Speaker: Libo Li (University of New South Wales)
• Title: multivariate analysis

• Date: 11 Sep. (Tue.)
• Place: W.W. 6th-floor, Colloquium Room
• Time: 14:00-
• Speaker: Arturo Kohatsu-Higa (Ritsumeikan University)
• Title: regression analysis

• Date: 30 Aug. (Thu.)
• Place: W.W. 6th-floor, Colloquium Room
• Time: 16:30-18:00
• Speaker: Makoto Yamazato (Tokyo Woman’s Christian University)
• Title: Boundedness of the densities of CME-subordinators

• This seminar was canceled.