Browsing by Author "Yau, Horng-Tzer"
Now showing items 21-40 of 49
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Logarithmic Sobolev inequality for lattice gases with mixing conditions
Yau, Horng-Tzer (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 ... -
Logarithmic Sobolev inequality for some models of random walks
Yau, Horng-Tzer; Lee, Tzong-Yow (Institute of Mathematical Statistics, 1998)We determine the logarithmic Sobolev constant for the Bernoulli- Laplace model and the time to stationarity for the symmetric simple exclusion model up to the leading order. Our method for proving the logarithmic Sobolev ... -
(logt)2/3 law of the two dimensional asymmetric simple exclusion process
Yau, Horng-Tzer (Annals of Mathematics, Princeton U, 2004)We prove that the diffusion coefficient for the two dimensional asymmetric simple exclusion process diverges as (logt)2/3 to the leading order. The method applies to nearest and non-nearest neighbor asymmetric simple ... -
Lower Bound on the Blow-up Rate of the Axisymmetric Navier-Stokes Equations
Chen, C.-C.; Strain, R. M.; Yau, Horng-Tzer; Tsai, T.-P. (Oxford University Press (OUP), 2010)Consider axisymmetric strong solutions of the incompressible Navier-Stokes equations in R 3 with non-trivial swirl. Such solutions are not known to be globally defined, but it is shown in [11, 1] that they could only blow ... -
Lower Bounds on the Blow-Up Rate of the Axisymmetric Navier–Stokes Equations II
Chen, Chiun-Chuan; Strain, Robert M.; Tsai, Tai-Peng; Yau, Horng-Tzer (Informa UK Limited, 2009)Consider axisymmetric strong solutions of the incompressible Navier–Stokes equations in ℝ3 with non-trivial swirl. Let z denote the axis of symmetry and r measure the distance to the z-axis. Suppose the solution satisfies, ... -
Nonlinear Hartree Equation as the Mean Field Limit of Weakly Coupled Fermions
Elgart, Alexander; Erdos, Laszlo; Schlein, Benjamin; Yau, Horng-Tzer (Elsevier BV, 2004)We consider a system of N weakly interacting fermions with a real analytic pair interaction. We prove that for a general class of initial data there exists a fixed time T such that the difference between the one particle ... -
On the Quantum Boltzmann Equation
Erdos, Laszlo; Salmhofer, Manfred; Yau, Horng-Tzer (Springer Nature, 2004)We give a nonrigorous derivation of the nonlinear Boltzmann equation from the Schrödinger evolution of interacting fermions. The argument is based mainly on the assumption that a quasifree initial state satisfies a property ... -
Quantum Diffusion for the Anderson Model in the Scaling Limit
Erdos, Laszlo; Salmhofer, Manfred; Yau, Horng-Tzer (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 ... -
Quantum diffusion of the random Schrödinger evolution in the scaling limit
Erdos, Laszlo; Salmhofer, Manfred; Yau, Horng-Tzer (International Press of Boston, 2008)We consider random Schrödinger equations on Rd for d ≽ 3 with a homogeneous Anderson–Poisson type random potential. Denote by λ the coupling constant and ψtψt the solution with initial data ψ0ψ0 . The space and time ... -
Quantum Diffusion of the Random Schrödinger Evolution in the Scaling Limit II. The Recollision Diagrams
Erdos, Laszlo; Salmhofer, Manfred; Yau, Horng-Tzer (Springer Nature, 2007)We consider random Schrödinger equations on {mathbb{R}d} for d≥ 3 with a homogeneous Anderson-Poisson type random potential. Denote by λ the coupling constant and ψ t the solution with initial data ψ0. The space and time ... -
Relaxation of excited states in nonlinear Schrödinger equations
Tsai, Tai-Peng; Yau, Horng-Tzer (Oxford University Press (OUP), 2002)We consider a nonlinear Schrödinger equation with a bounded local potential in ℝ3. The linear Hamiltonian is assumed to have two bound states with the eigenvalues satisfying some resonance condition. Suppose that the initial ... -
Relaxation to Equilibrium of Conservative Dynamics. I: Zero-Range Processes
Janvresse, E.; Landim, C.; Quastel, J.; Yau, Horng-Tzer (Institute of Mathematical Statistics, 1999)Under mild assumptions we prove that for any local function uu the decay rate to equilibrium in the variance sense of zero range dynamics on dd-dimensional integer lattice is Cut−d/2+o(t−d/2)Cut−d/2+o(t−d/2). The constant ... -
Rigidity of Eigenvalues of Generalized Wigner Matrices
Erdos, Laszio; Yau, Horng-Tzer; Yin, Jun (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 ... -
Rigorous Derivation of the Gross-Pitaevskii Equation
Erdős, László; Schlein, Benjamin; Yau, Horng-Tzer (American Physical Society (APS), 2007)The time-dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schrödinger equation with a ... -
A rigorous examination of the Chandrasekhar theory of stellar collapse
Lieb, Elliott H.; Yau, Horng-Tzer (IOP Publishing, 1987) -
The Second Order Upper Bound for the Ground Energy of a Bose Gas
Yau, Horng-Tzer; Yin, Jun (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 ... -
Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices
Erdős, László; Schlein, Benjamin; Yau, Horng-Tzer (Institute of Mathematical Statistics, 2009)We consider N×N Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order 1/N. We study the connection between eigenvalue statistics on ... -
Several Theorems About Probabilistic Limiting Expressions: The Gaussian free field, symmetric Pearcey process, and strong Szegő asymptotics
Kuan, Jeffrey (2015-04-30)Certain probabilistic processes appear in the asymptotic scaling limit of many models. This thesis covers several theorems about such processes. Chapter 2 covers the Gaussian free field in interlacing particle systems, ... -
Spectral Statistics of Erdős-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues
Erdos, Laszlo; Knowles, Antti; Yau, Horng-Tzer; Yin, Jun (Springer Nature, 2012)We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, i.e. graphs on N vertices where every edge is chosen independently and with probability p ≡ p(N). We rescale the matrix so that its bulk eigenvalues ...