Tracy-Widom distribution was rst 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 elds.It is...Tracy-Widom distribution was rst 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 elds.It is believed that Tracy-Widom distribution have a universal feature like classic normal distribution.Airy2 process is de ned through nite dimensional distributions with Tracy-Widom distribution as its marginal distributions.In this introductory survey,we will briey 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.展开更多
The Hansdorff dimensions of the image and the graph of random fields are given under general conditions.The results can be used to a wider class of self-similar random fields and processes,including Brownian motion,Br...The Hansdorff dimensions of the image and the graph of random fields are given under general conditions.The results can be used to a wider class of self-similar random fields and processes,including Brownian motion,Brownian sheet,fractional Brownian motion,processes with stable or(α,β)-fractional stable components.展开更多
基金the National Natural Science Foundation of China(11731012,11871425)Fundamental Research Funds for Central Universities grant(2020XZZX002-03).
文摘Tracy-Widom distribution was rst 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 elds.It is believed that Tracy-Widom distribution have a universal feature like classic normal distribution.Airy2 process is de ned through nite dimensional distributions with Tracy-Widom distribution as its marginal distributions.In this introductory survey,we will briey 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.
基金Supported by the National Natural Science Foundation of China.
文摘The Hansdorff dimensions of the image and the graph of random fields are given under general conditions.The results can be used to a wider class of self-similar random fields and processes,including Brownian motion,Brownian sheet,fractional Brownian motion,processes with stable or(α,β)-fractional stable components.
