포항공과대학교 수학과

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분야Field	2017 Math Colloquium
날짜Date	2017-12-01	시간Time	15:50 ~ 18:00
장소Place	Math. Bldg. 404	초청자Host	김건우
연사Speaker	Paul Jung	소속Affiliation	KAIST
TOPIC	Levy-Khintchine Random Matrices
소개 및 안내사항Content	Title : Levy-Khintchine Random Matrices. Abstract: We study a class of Hermitian random matrices which includes Wigner matrices, heavy-tailed random matrices, and sparse random matrices such as adjacency matrices of Erdos-Renyi 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 well-known 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 semi-circle law.

분야Field

2017 Math Colloquium

날짜Date

2017-12-01

시간Time

15:50 ~ 18:00

장소Place

Math. Bldg. 404

초청자Host

김건우

연사Speaker

Paul Jung

소속Affiliation

KAIST

TOPIC

Levy-Khintchine Random Matrices

소개 및 안내사항Content

Title : Levy-Khintchine Random Matrices.

Abstract: We study a class of Hermitian random matrices which includes Wigner matrices, heavy-tailed random matrices, and sparse random matrices such as adjacency matrices of Erdos-Renyi 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 well-known 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 semi-circle law.

일시Date	제목Title	연사Speaker	장소Place
2017-12-08	2017 Math Colloquium \| Volumes of hyperbolic manifolds 관리자 \| 2017.12.04 \| 추천 -1 \| 조회 1285	BoGwang Jeon	Math. Bldg. 404
2017-12-01	2017 Math Colloquium \| Levy-Khintchine Random Matrices 관리자 \| 2017.11.16 \| 추천 -1 \| 조회 1018	Paul Jung	Math. Bldg. 404
2017-11-10	2017 Math Colloquium \| Simple zeros of L-functions 관리자 \| 2017.10.31 \| 추천 -1 \| 조회 907	Jaehyun Cho	Math. Bldg. 404
2017-10-20	2017 Math Colloquium \| The irrationality exponent of real numbers and the expansion in integer base 관리자 \| 2017.10.16 \| 추천 -1 \| 조회 785	Dong Han Kim	Math. Bldg. 404
2017-10-13	2017 Math Colloquium \| Ⅰ: Operator Algebras, Groups and Quantum Probability 1 , ∥: Operator Algebras, Groups and Quantum Probability 2 관리자 \| 2017.09.18 \| 추천 -1 \| 조회 866	Jaeseong Heo	Math. Bldg. 404
2017-09-15	2017 Math Colloquium \| Arithmetic Chern-Simons theory 관리자 \| 2017.09.11 \| 추천 1 \| 조회 890	Jeehoon Park	Math. Bldg. 404
2017-09-08	2017 Math Colloquium \| Existence, corner singularities and regularities of the compressible Stokes flows passing or through non-convex corner, cut and 관리자 \| 2017.08.23 \| 추천 -2 \| 조회 854	Jae Ryong Kwon	Math. Bldg. 404
2017-06-02	2017 Math Colloquium \| I: High-dimensionality, Uncertainty Quantification and Scientific Computing, II: Model Reduction for Stochastic Partial Differe sugarless \| 2017.04.03 \| 추천 -1 \| 조회 1193	Minseok Choi	Math Sci Bldg 404
2017-05-26	2017 Math Colloquium \| Representations of classical Lie algebras and combinatorics of their branching rules sugarless \| 2017.04.03 \| 추천 0 \| 조회 729	Jae-Hoon Kwon	Math Sci Bldg 404
2017-05-19	2017 Math Colloquium \| I:Arithmetic of special values of zeta functions, II:Arithmetic of several L-values sugarless \| 2017.04.03 \| 추천 0 \| 조회 603	Hae-Sang Sun	Math Sci Bldg 404

일시Date

제목Title

연사Speaker

장소Place

2017-12-08

2017 Math Colloquium | Volumes of hyperbolic manifolds

관리자 | 2017.12.04 | 추천 -1 | 조회 1285

BoGwang Jeon

Math. Bldg. 404

2017-12-01

2017 Math Colloquium | Levy-Khintchine Random Matrices

관리자 | 2017.11.16 | 추천 -1 | 조회 1018