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Mathematics Colloquium

Reda Chhaibi
Universite Toulouse, Paul Sabatier

Title: Is the Tracy-Widom distribution a coincidence or a law of nature
Date: Friday, November 22, 2019
Place and Time: Room 101, Love Building, 3:35-4:25 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. Why do certain probability distributions appear in nature, in seemingly different contexts? Three classical examples of laws of nature are: - the law of rare events aka the Poisson distribution. - the law of common events aka the Gaussian distribution. - the laws of extreme events (Gumbel, Weibull and Frechet). At least the two first laws are quickly derived thanks to harmonic analysis (Fourier analysis). In the recent history, a distribution called the Tracy-Widom distributions has appeared in various complex correlated systems. It is believed to be a universal law of nature. Two instances are: - random matrices when observing the largest eigenvalue. - last passage percolation when observing last passage times. In a seminal paper, Johansson notices a surprising equality in distribution between these quantities. His result was further strengthened by Dieker and Warren. After motivating and explaining these two different contexts, I will conclude by explaining why Johansson's equality can be seen as a rigidity property in (non-commutative) harmonic analysis.