Search
Now showing items 1-10 of 48
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 ...
The local relaxation flow approach to universality of the local statistics for random matrices
(Institute of Mathematical Statistics, 2012)
We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the ...
The Second Order Upper Bound for the Ground Energy of a Bose Gas
(Springer, 2009)
Consider \(N\) bosons in a finite box \(\Lambda= [0,L]^3\subset \mathbf R^3\) interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives the following upper bound on the ...
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 ...
Asymptotic dynamics of nonlinear Schrödinger equations: Resonance-dominated and dispersion-dominated solutions
(Wiley-Blackwell, 2001)
We consider a linear Schrödinger equation with a nonlinear perturbation in ℝ3. Assume that the linear Hamiltonian has exactly two bound states and its eigen-values satisfy some resonance condition. We prove that if the ...
Logarithmic Sobolev inequality for lattice gases with mixing conditions
(Springer Nature, 1996)
Let μgcΛL,λμΛL,λgc denote the grand canonical Gibbs measure of a lattice gas in a cube of sizeL with the chemical potential γ and a fixed boundary condition. Let μcΛL,nμΛL,nc be the corresponding canonical measure defined ...
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 ...