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In the theory of random matrices, the Gaussian matrix ensembles are Gaussian measures on spaces of Hermitian matrices T, obtained by multiplying a translation-invariant measure by the Gaussian function exp(−Tr(T2)). The three main examples are the Gaussian orthogonal ensemble on real Hermitian matrices, the Gaussian unitary ensemble on complex Hermitian matrices, and the Gaussian symplectic ensemble on quaternionic Hermitian matrices. The Tracy–Widom distributions Fβ, β = 1, 2, 4, govern the distribution of the largest eigenvalue of a random matrix in the each of these three Gaussian ensembles. However, other mathematical objects have the same distribution as well; for instance, F2 provides the limiting distribution on the length of the longest increasing subsequence of random permutations (Baik, Deift & Johansson 1999). See also Circular ensemble References Baik, Jinho; Deift, Percy; Johansson, Kurt (1999), "On the distribution of the length of the longest increasing subsequence of random permutations", Journal of the American Mathematical Society 12 (4): 1119–1178, doi:10.1090/S0894-0347-99-00307-0, MR1682248, ISSN 0894-0347, http://www.jstor.org/stable/2646100  arXiv:math/9810105. Fyodorov, Yan V. (2005), "Introduction to the random matrix theory: Gaussian unitary ensemble and beyond", Recent perspectives in random matrix theory and number theory, London Math. Soc. Lecture Note Ser., 322, Cambridge University Press, pp. 31–78, MR2166458, http://arxiv.org/abs/math-ph/0412017  Mehta, Madan Lal (2004), Random matrices, Pure and Applied Mathematics (Amsterdam), 142 (3rd ed.), Elsevier/Academic Press, Amsterdam, MR2129906, ISBN 978-0-12-088409-4