平成30年度学習院大学スペクトル理論セミナー


第165回学習院大学スペクトル理論セミナー

日時:2018 年 6月 9 日 (土) 15:00 -- 17:30
場所: 学習院大学 南4号館2階 205セミナー室

1. 15:00--16:00
講演者: Khanh Duy Trinh氏 (東北大・理)

Title:Classical beta ensembles in global regime

Abstract: Gaussian beta ensembles, Wishart beta ensembles and Jacobi beta ensembles are three typical examples of beta ensembles on the real line. The limiting behavior of the empirical distribution, the probability measure putting equal mass at each eigenvalue, is one of fundamental problem in studying a random matrix model. Based on their random tridiagonal matrix models, this talk introduces a unify approach to completely solve that problem.The result can be shortly mentioned as follows. The limit of the empirical distribution depends only on the limit of the coupling \( n \beta \): zero, finite or infinite. Here \(n\) is the system size, or the order of a random matrix, and \( n \beta \) is a parameter regarded as the inverse temperature of the system. In particular, the case where \( n \beta \) tends to infinity is similar to the case of fixed beta. When \( n \beta \) tends to a finite constant, the limiting distribution is an associated version of the corresponding weight in the sense of orthogonal polynomials.

16:00--16:30 tea time

2. 16:30--17:30
講演者: 上木 直昌氏 (京都大・人間環境)

Title: Asymptotic behavior of the integrated density of states of a Schrödinger operator with positive potentials located around all sample points of some random point field

Abstract:Asymptotic behavior of the integrated density of states of a Schrödinger operator with positive potentials located around all sample points of some random point field at the infimum of the spectrum is investigated. The random point field is taken from a subclass of the class given by Shirai and Takahashi in terms of the Fredholm determinant. In the subclass, the obtained leading orders are same with the well known results for the Poisson point fields, and the character of the random field appears in the leading constants. The random point field associated with the sine kernel and the Ginibre random point field are well studied examples not included in the above subclass, though they are included in the class by Shirai and Takahashi. By applying the results on asymptotics of the hole probability for these random fields, the corresponding asymptotic behaviors of the densities of the states are also investigated in the case where the single site potentials have compact supports.


昨年度までの記録

平成29年度 平成28年度 平成27年度 平成26年度 平成25年度

平成24年度 平成23年度 平成22年度 平成21年度 平成20年度

平成19年度 平成18年度 平成17年度 平成16年度 平成15年度

平成14年度 平成13年度

 


連絡先:学習院大学理学部数学教室
TEL: 03-3986-0221 内線 3702(谷島賢二) 6443(中野(史))

e-mail: (あっと)を @ に書き直してください。