Tracy-Widom distribution, Airy2 process and its sample path properties

Autor:	Tian Shen, Zhong-gen Su, Yu-huan Lei
Rok vydání:	2021
Předmět:	Normal distribution symbols.namesake Distribution (number theory) Tracy–Widom distribution Simple (abstract algebra) Applied Mathematics Gaussian symbols Statistical physics Marginal distribution Gaussian process Eigenvalues and eigenvectors Mathematics
Zdroj:	Applied Mathematics-A Journal of Chinese Universities. 36:128-158
ISSN:	1993-0445 1005-1031
DOI:	10.1007/s11766-021-4251-2
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::770f353a78214a7f30b83783b9ca983f https://doi.org/10.1007/s11766-021-4251-2 Zobrazit plný text záznamu Full text from SpringerLink