论文信息 - The right tail exponent of the Tracy–Widom $\beta$ distribution

The right tail exponent of the Tracy–Widom $\beta$ distribution

The Tracy-Widom beta distribution is the large dimensional limit of the top eigenvalue of beta random matrix ensembles. We use the stochastic Airy operator representation to show that as a tends to infinity the tail of the Tracy Widom distribution satisfies P(TW_beta > a) = a^(-3/4 beta+o(1)) exp(-2/3 beta a^(3/2)).

B'alint Vir'ag | Laure Dumaz | B'alint Vir'ag | Laure Dumaz

[1] C. Tracy,et al. Mathematical Physics © Springer-Verlag 1996 On Orthogonal and Symplectic Matrix Ensembles , 1995 .

[2] B. Eynard,et al. Topological expansion of the β-ensemble model and quantum algebraic geometry in the sectorwise approach , 2010, 1009.6007.

[3] J. Ramírez,et al. Beta ensembles, stochastic Airy spectrum, and a diffusion , 2006, math/0607331.

[4] B'alint Vir'ag,et al. Large gaps between random eigenvalues. , 2008, 0811.0007.

[5] S. Majumdar,et al. Large deviations of the maximal eigenvalue of random matrices , 2010, 1009.1945.

[6] Леонид Олегович Чехов,et al. Топологическое разложение модели $\beta$-ансамбля и квантовая алгебраическая геометрия в рамках секторного подхода@@@Topological expansion of the $\beta$-ensemble model and quantum algebraic geometry in the sectorwise approach , 2011 .

[7] Jinho Baik,et al. Asymptotics of Tracy-Widom Distributions and the Total Integral of a Painlevé II Function , 2007, 0704.3636.

[8] F. Dyson. Statistical Theory of the Energy Levels of Complex Systems. I , 1962 .

[9] Y Chen,et al. Some eigenvalue distribution functions of the Laguerre ensemble , 1996 .

[10] P. Forrester. Log-Gases and Random Matrices , 2010 .

[11] A. Edelman,et al. Matrix models for beta ensembles , 2002, math-ph/0206043.