Abstract
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.
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22 June 2021
An Erratum to this paper has been published: https://doi.org/10.1007/s11766-021-4473-3
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Acknowledgement
Z.G.Su wishes to express his best gratitude to Yimin Xiao for his instructive comments on sample paths properties of random processes. The authors are grateful to the anonymous referee for careful reading.
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Supported by the National Natural Science Foundation of China(11731012, 11871425) and Fundamental Research Funds for Central Universities grant(2020XZZX002-03).
The original version of this article was revised due to a retrospective Open Access order.
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Su, Zg., Lei, Yh. & Shen, T. Tracy-Widom distribution, Airy2 process and its sample path properties. Appl. Math. J. Chin. Univ. 36, 128–158 (2021). https://doi.org/10.1007/s11766-021-4251-2
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DOI: https://doi.org/10.1007/s11766-021-4251-2