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

• 来源期刊: 高校应用数学学报B辑（英文版）
• 年，卷（期）: 2021,（1）
• 页码范围: 128-158
• 页数: 31页
• 语种: 英文
• DOI: 10.1007/s11766-021-4251-2

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 funda-mental 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.