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From Gumbel to TracyWidom
"... Abstract. The TracyWidom distribution that has been much studied in recent years can be thought of as an extreme value distribution. We discuss interpolation between the classical extreme value distribution exp( − exp(−x)), the Gumbel distribution and the TracyWidom distribution. There is a family ..."
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Abstract. The TracyWidom distribution that has been much studied in recent years can be thought of as an extreme value distribution. We discuss interpolation between the classical extreme value distribution exp( − exp(−x)), the Gumbel distribution and the TracyWidom distribution. There is a
DISCRETE TRACY–WIDOM OPERATORS
, 806
"... Abstract Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large selfadjoint random matrices from the generalized unitary ensembles. This paper considers discrete Tracy–Widom operators, and gives sufficient conditions for a discrete in ..."
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Abstract Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large selfadjoint random matrices from the generalized unitary ensembles. This paper considers discrete Tracy–Widom operators, and gives sufficient conditions for a discrete
TRACYWIDOM AT HIGH TEMPERATURE
"... Abstract. We investigate the marginal distribution of the bottom eigenvalues of the stochastic Airy operator when the inverse temperature β tends to 0. We prove that the minimal eigenvalue, whose fluctuations are governed by the TracyWidom β law, converges weakly, when properly centered and scaled, ..."
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Abstract. We investigate the marginal distribution of the bottom eigenvalues of the stochastic Airy operator when the inverse temperature β tends to 0. We prove that the minimal eigenvalue, whose fluctuations are governed by the TracyWidom β law, converges weakly, when properly centered and scaled
The right tail exponent of the TracyWidomβ distribution
, 2011
"... TheTracyWidom β distributionis thelarge dimensional limit of the top eigenvalue of β random matrix ensembles. We use the stochastic Airy operator representation to show that as a → ∞ the tail of the Tracy Widom distribution satisfies P (TWβ> a) = a −3 ..."
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TheTracyWidom β distributionis thelarge dimensional limit of the top eigenvalue of β random matrix ensembles. We use the stochastic Airy operator representation to show that as a → ∞ the tail of the Tracy Widom distribution satisfies P (TWβ> a) = a −3
A determinantal formula for the GOE TracyWidom distribution
 J. Phys. A
"... Investigating the long time asymptotics of the totally asymmetric simple exclusion process, Sasamoto obtains rather indirectly a formula for the GOE TracyWidom distribution. We establish that his novel formula indeed agrees with more standard expressions. 1 ..."
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Cited by 36 (13 self)
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Investigating the long time asymptotics of the totally asymmetric simple exclusion process, Sasamoto obtains rather indirectly a formula for the GOE TracyWidom distribution. We establish that his novel formula indeed agrees with more standard expressions. 1
Asymptotics of TracyWidom distributions and the total integral of a Painlevé
 II function, Comm. Math. Phys
"... The TracyWidom distribution functions involve integrals of a Painlevé II function starting from positive infinity. In this paper, we express the TracyWidom distribution functions in terms of integrals starting from minus infinity. There are two consequences of these new representations. The first ..."
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Cited by 37 (3 self)
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The TracyWidom distribution functions involve integrals of a Painlevé II function starting from positive infinity. In this paper, we express the TracyWidom distribution functions in terms of integrals starting from minus infinity. There are two consequences of these new representations. The first
Accuracy of the TracyWidom limit for the largest eigenvalue in white Wishart matrices
, 2008
"... Let A be a pvariate real Wishart matrix on n degrees of freedom with identity covariance. The distribution of the largest eigenvalue in A has important applications in multivariate statistics. Consider the asymptotics when p grows in proportion to n, it is known from Johnstone (2001) that after cen ..."
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Cited by 5 (0 self)
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centering and scaling, these distributions approach the orthogonal TracyWidom law for realvalued data, which can be numerically evaluated and tabulated in software. Under the same assumption, we show that more carefully chosen centering and scaling constants improve the accuracy of the distributional
Convergence to the TracyWidom distribution for longest paths in a directed random graph
"... Abstract. We consider a directed graph on the 2dimensional integer lattice, placing a directed edge from vertex (i1; i2) to (j1; j2), whenever i1 j1, i2 j2, with probability p, independently for each such pair of vertices. Let Ln;m denote the maximum length of all paths contained in an nm rectan ..."
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rectangle. We show that there is a positive exponent a, such that, if m=na! 1, as n! 1, then a properly centered/rescaled version of Ln;m converges weakly to the TracyWidom distribution. A generalization to graphs with nonconstant probabilities is also discussed.
Results 1  10
of
1,477