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Applied Mathematics-A Journal of Chinese Universities  2021, Vol. 36 Issue (1): 128-158    
    
Tracy-Widom distribution, Airy2 process and its sample path properties
SU Zhong-gen, LEI Yu-huan, SHEN Tian
School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China.
Tracy-Widom distribution, Airy2 process and its sample path properties
SU Zhong-gen, LEI Yu-huan, SHEN Tian
School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China.
 全文: PDF 
摘要： Tracy-Widom distribution was first discovered in the study of largest eigenvalues
of high dimensional Gaussian unitary ensembles (GUE), and since then it has appeared in a
number of apparently distinct research fields. It is believed that Tracy-Widom distribution
have a universal feature like classic normal distribution. Airy2 process is defined through finite
dimensional distributions with Tracy-Widom distribution as its marginal distributions. In this
introductory survey, we will briefly review some basic notions, intuitive background and fundamental properties concerning Tracy-Widom distribution and Airy2 process. For sake of reading,
the paper starts with some simple and well-known facts about normal distributions, Gaussian
processes and their sample path properties.
关键词： Airy2 process;  Dyson Brownian motion;  Tracy-Widom distribution;  sample path property    
Abstract: Tracy-Widom distribution was first discovered in the study of largest eigenvalues
of high dimensional Gaussian unitary ensembles (GUE), and since then it has appeared in a
number of apparently distinct research fields. It is believed that Tracy-Widom distribution
have a universal feature like classic normal distribution. Airy2 process is defined through finite
dimensional distributions with Tracy-Widom distribution as its marginal distributions. In this
introductory survey, we will briefly review some basic notions, intuitive background and fundamental properties concerning Tracy-Widom distribution and Airy2 process. For sake of reading,
the paper starts with some simple and well-known facts about normal distributions, Gaussian
processes and their sample path properties.
Key words: Airy2 process    Dyson Brownian motion    Tracy-Widom distribution    sample path property
出版日期: 2021-03-19
CLC:  60K35  
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SU Zhong-gen
LEI Yu-huan
SHEN Tian

引用本文:

SU Zhong-gen, LEI Yu-huan, SHEN Tian. Tracy-Widom distribution, Airy2 process and its sample path properties[J]. Applied Mathematics-A Journal of Chinese Universities, 2021, 36(1): 128-158.

SU Zhong-gen, LEI Yu-huan, SHEN Tian. Tracy-Widom distribution, Airy2 process and its sample path properties. Applied Mathematics-A Journal of Chinese Universities, 2021, 36(1): 128-158.

链接本文:

http://www.zjujournals.com/amjcub/CN/    或    http://www.zjujournals.com/amjcub/CN/Y2021/V36/I1/128

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