Search
Now showing items 1-10 of 24
Bulk universality for generalized Wigner matrices
(Springer Science + Business Media, 2011)
Consider \(N × N\) Hermitian or symmetric random matrices H where the distribution of the (i, j) matrix element is given by a probability measure \(\nu_{ij}\) with a subexponential decay. Let \(\sigma_{ij}^2\) be the ...
Rigidity of Eigenvalues of Generalized Wigner Matrices
(Elsevier BV, 2012)
Consider \(N\times N\) hermitian or symmetric random matrices \(H\) with independent entries, where the distribution of the \((i,j)\) matrix element is given by the probability measure \(\nu_{ij}\) with zero expectation ...
Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation
(Institute of Mathematical Statistics, 2010)
We consider N×N Hermitian random matrices with independent identically distributed entries (Wigner matrices). We assume that the distribution of the entries have a Gaussian component with variance N−3/4+βN−3/4+β for some ...
Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate
(Annals of Mathematics, Princeton U, 2010)
Consider a system of N bosons in three dimensions interacting via a repulsive short range pair potential N²V (N(xi − xj)), where x = (x1,..., xN) denotes the positions of the particles. Let HN denote the Hamiltonian of the ...
Local Semicircle Law and Complete Delocalization for Wigner Random Matrices
(Springer Nature, 2008)
We consider N × N Hermitian random matrices with independent identical distributed entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order 1/N. Under suitable assumptions ...
Quantum Diffusion for the Anderson Model in the Scaling Limit
(Springer Nature, 2007)
We consider random Schrödinger equations on ℤdZd for d ≥ 3 with identically distributed random potential. Denote by λ the coupling constant and ψt the solution with initial data ψ0. The space and time variables scale as ...
Bulk universality for Wigner matrices
(Wiley-Blackwell, 2010)
We consider N × N Hermitian Wigner random matrices H where the probability density for each matrix element is given by the density ν(x) = e−U(x). We prove that the eigenvalue statistics in the bulk are given by the Dyson ...
Universality of general β-ensembles
(Duke University Press, 2014)
We prove the universality of the β-ensembles with convex analytic potentials and for any β>0; that is, we show that the spacing distributions of log-gases at any inverse temperature β coincide with those of the Gaussian ...
Towards the Quantum Brownian Motion
(Springer Berlin Heidelberg, 2006)
We consider random Schr\"odinger equations on $\bR^d$ or $\bZ^d$ for d≥3 with uncorrelated, identically distributed random potential. Denote by λ the coupling constant and ψt the solution with initial data ψ0. Suppose that ...
Bulk universality of general β-ensembles with non-convex potential
(AIP Publishing, 2012-09)
We prove the bulk universality of the β-ensembles with non-convex regular analytic potentials for any β > 0. This removes the convexity assumption appeared in the earlier work [P. Bourgade, L. Erdös, and H.-T. Yau, ...