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

Abstract Tracy-Widom distribution was first discovered in the study of largest eigenvalues high dimensional Gaussian unitary ensembles (GUE), and since then it has appeared a number apparently distinct research fields. It is believed that have universal feature like classic normal distribution. Airy 2 process defined through finite distributions with as its marginal distributions. In this introductory survey, we will briefly review some basic notions, intuitive background fundamental properties concerning process. For sake reading, paper starts simple well-known facts about distributions, processes their sample path properties.