포항공과대학교 수학과

Board

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
2018-06-01	2018 Math Colloquim \| Why do we study local fields? 수학과 \| 2018.05.28 \| 추천 0 \| 조회 845	Sungmun Cho	Math. Bldg. 404
2018-05-25	2018 Math Colloquim \| Busemann's intersection inequality in non-Euclidean spaces 수학과 \| 2018.05.23 \| 추천 0 \| 조회 597	Jaegil Kim	Math. Bldg. 404
2018-05-18	2018 Math Colloquim \| Universality of random graphs and random intersection graphs related to MERS 수학과 \| 2018.04.27 \| 추천 0 \| 조회 651	Sang June Lee	Math. Bldg. 404
2018-04-20	2018 Math Colloquim \| Policy gradient methods for reinforcement learning 수학과 \| 2018.04.17 \| 추천 0 \| 조회 684	Kee-Ung Kim	Math. Bldg. 404
2018-04-06	2018 Math Colloquim \| Introduction to Okounkov bodies 수학과 \| 2018.04.03 \| 추천 -5 \| 조회 734	Sung Rak Choi	Math. Bldg. 404
2018-03-30	2018 Math Colloquium \| Climate Complexity( A journey into ocean mud, ice cores, supercomputing and bifurcation analysis ) 관리자 \| 2018.03.28 \| 추천 -2 \| 조회 772	Axel Timmermann	Math. Bldg. 404
2018-03-23	2018 Math Colloquium \| Classical and Quantum White Noise Theory 수학과 \| 2018.03.19 \| 추천 -1 \| 조회 765	Un Cig Ji	Math. Bldg. 404
2018-03-16	2018 Math Colloquium \| Torus actions and dynamical systems 수학과 \| 2018.03.12 \| 추천 -1 \| 조회 692	Nguyen TienZung	Math. Bldg. 404
2018-03-09	2018 Math Colloquium \| Mathematics of Medical Image Analysis and Machine Learning 수학과 \| 2018.03.02 \| 추천 -1 \| 조회 713	Jin Keun Seo	Math. Bldg. 404
2018-02-23	2018 Math Colloquium \| A question of John Milnor and localization of groups 수학과 \| 2018.02.20 \| 추천 -1 \| 조회 679	Jae Choon Cha	Math. Bldg. 404

일시Date

제목Title

연사Speaker

장소Place

2018-06-01

2018 Math Colloquim | Why do we study local fields?

수학과 | 2018.05.28 | 추천 0 | 조회 845

Sungmun Cho

Math. Bldg. 404

2018-05-25

2018 Math Colloquim | Busemann's intersection inequality in non-Euclidean spaces

수학과 | 2018.05.23 | 추천 0 | 조회 597