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CLT for linear spectral statistics of random matrix $S^{-1}T$
CLT linear spectral statistics random matrix $S^{-1}T$
2013/6/13
This paper proposes a CLT for linear spectral statistics of random matrix $S^{-1}T$ for a general non-negative definite and {\bf non-random} Hermitian matrix $T$.
A Note on Central Limit Theorems for Linear Spectral Statistics of Large Dimensional F-matrix
Linear spectral statistics central limit theorem centralized sample covari-ance matrix centralizedF-matrix simplified sample covariance matrix simplified F-matrix
2013/6/13
Sample covariance matrix and multivariate $F$-matrix play important roles in multivariate statistical analysis. The central limit theorems {\sl (CLT)} of linear spectral statistics associated with the...
Random matrices: Universality of local spectral statistics of non-Hermitian matrices
Random matrices non-Hermitian matrices Probability
2012/6/30
It is a classical result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n \times n$ gaussian matrix with independent entries of mean zero and unit variance are asymp...
Universality of local spectral statistics of random matrices
Random matrix Local semicircle law Tracy-Widom distribution Dyson Brownian motion
2011/7/28
Abstract: The Wigner-Gaudin-Mehta-Dyson conjecture asserts that the local eigenvalue statistics of large random matrices exhibit universal behavior depending only on the symmetry class of the matrix e...
Spectral Statistics of "Cellular" Billiards
Chaotic Dynamics(nlin.CD) Mathematical Physics(math-ph) Spectral Theory(math.SP)
2010/11/10
For a bounded planar domain $\Omega^0$ whose boundary contains a number of flat pieces $\Gamma_i$ we consider a family of non-symmetric billiards $\Omega$ constructed by patching several copies of $\O...
Spectral statistics for random Schrödinger operators in the localized regime
Spectral statistics random Schrö dinger operators the localized regime
2010/11/15
We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy $E$ in the localized phase. Assume ...