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