Colloquium
LevyKhintchine Random Matrices
작성자Author
관리자
작성일Date
20171116 09:00
조회Views
619
분야Field  2017 Math Colloquium  

날짜Date  20171201  시간Time  15:50 ~ 18:00 
장소Place  Math. Bldg. 404  초청자Host  김건우 
연사Speaker  Paul Jung  소속Affiliation  KAIST 
TOPIC  LevyKhintchine Random Matrices  
소개 및 안내사항Content  Title : LevyKhintchine Random Matrices. Abstract: We study a class of Hermitian random matrices which includes Wigner matrices, heavytailed random matrices, and sparse random matrices such as adjacency matrices of ErdosRenyi graphs with p=1/N. Our matrices have real entries which are i.i.d. up to symmetry. The distribution of entries depends on N, and we require sums of rows to converge in distribution; it is then wellknown that the limit must be infinitely divisible. We show that a limiting empirical spectral distribution (LSD) exists, and via local weak convergence of associated graphs, the LSD corresponds to the spectral measure associated to the root of a graph which is formed by connecting infinitely many Poisson weighted infinite trees using a backbone structure of special edges. One example covered are matrices with i.i.d. entries having infinite second moments, but normalized to be in the Gaussian domain of attraction. In this case, the LSD is a semicircle law. 
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