Universality for the Toda algorithm to compute the eigenvalues of a random matrix
暂无分享,去创建一个
[1] M. Toda. Vibration of a Chain with Nonlinear Interaction , 1967 .
[2] S. Manakov. Complete integrability and stochastization of discrete dynamical systems , 1974 .
[3] H. Flaschka. The Toda lattice. II. Existence of integrals , 1974 .
[4] J. Moser,et al. Three integrable Hamiltonian systems connected with isospectral deformations , 1975 .
[5] Mark Adler,et al. On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-devries type equations , 1978 .
[6] B. Kostant,et al. The solution to a generalized Toda lattice and representation theory , 1979 .
[7] A. J. Stam. LIMIT THEOREMS FOR UNIFORM DISTRIBUTIONS ON SPHERES IN HIGH-DIMENSIONAL EUCLIDEAN SPACES , 1982 .
[8] P. Deift,et al. Ordinary differential equations and the symmetric eigenvalue problem , 1983 .
[9] Carlos Tomei,et al. Toda flows with infinitely many variables , 1985 .
[10] Carlos Tomei,et al. The toda flow on a generic orbit is integrable , 1986 .
[11] C. Tracy,et al. Level-spacing distributions and the Airy kernel , 1992, hep-th/9211141.
[12] David S. Watkins. Isospectral Flows , 1996 .
[13] A. Soshnikov. Universality at the Edge of the Spectrum¶in Wigner Random Matrices , 1999, math-ph/9907013.
[14] P. Deift. Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach , 2000 .
[15] Universality at the edge of the spectrum for unitary, orthogonal, and symplectic ensembles of random matrices , 2005, math-ph/0507023.
[16] Tiefeng Jiang,et al. How many entries of a typical orthogonal matrix can be approximated by independent normals , 2006 .
[17] H. Yau,et al. Rigidity of eigenvalues of generalized Wigner matrices , 2010, 1007.4652.
[18] T. Tao,et al. Random Matrices: Universality of Local Eigenvalue Statistics up to the Edge , 2009, 0908.1982.
[19] J. Ramírez,et al. Beta ensembles, stochastic Airy spectrum, and a diffusion , 2006, math/0607331.
[20] Joshua Correll,et al. A neural computation model for decision-making times , 2012 .
[21] L. Erdős,et al. Universality for random matrices and log-gases , 2012, 1212.0839.
[22] P. J. Forrester,et al. Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles , 2012, 1209.2190.
[23] T. Garel,et al. Typical versus averaged overlap distribution in spin glasses: Evidence for droplet scaling theory , 2013, 1306.0423.
[24] H. Yau,et al. The Eigenvector Moment Flow and Local Quantum Unique Ergodicity , 2013, 1312.1301.
[25] H. Yau,et al. Edge Universality of Beta Ensembles , 2013, 1306.5728.
[26] G. Schehr,et al. Near-Extreme Eigenvalues and the First Gap of Hermitian Random Matrices , 2013, 1312.2966.
[27] P. Deift,et al. Universality in numerical computations with random data , 2014, Proceedings of the National Academy of Sciences.
[28] Yann LeCun,et al. Universality in halting time and its applications in optimization , 2015, ArXiv.
[29] P. Deift,et al. On the condition number of the critically-scaled Laguerre Unitary Ensemble , 2015, 1507.00750.
[30] P. Deift,et al. How long does it take to compute the eigenvalues of a random, symmetric matrix? , 2012, 1203.4635.