344 citations · 3.1k across the 86 of their papers we have counts for
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Operator Norm Bounds on the Correlation Matrix of the SK Model at High Temperature
Christian Brennecke, Changji Xu, Horng-Tzer Yau
We prove that the two point correlation matrix of the Sherrington-Kirkpatrick model has the p…
The Two Point Function of the SK Model without External Field at High Temperature
Christian Brennecke, Adrien Schertzer, Changji Xu +1
We show that the two point correlation matrix of the Sherrington-Kirkpatrick model with zero external field satisfies \[…
The Replica Symmetric Formula for the SK Model Revisited
Christian Brennecke, Horng-Tzer Yau
We provide a simple extension of Bolthausen's Morita type proof of the replica symmetric formula [E. Bolthausen, Stat. Mech. of Classical and Disordered Systems, pp. 63-93 (2018)]…
Dynamical Approach to the TAP Equations for the Sherrington-Kirkpatrick Model
Arka Adhikari, Christian Brennecke, Per von Soosten +1
We present a new dynamical proof of the Thouless-Anderson-Palmer (TAP) equations for the classical Sherrington-Kirkpatrick spin glass at sufficiently high temperature. In our deriv…
Global eigenvalue distribution of matrices defined by the skew-shift
Arka Adhikari, Marius Lemm, Horng-Tzer Yau
We consider large Hermitian matrices whose entries are defined by evaluating the exponential function along orbits of the skew-shift for irrational …
Local density for two-dimensional one-component plasma
Roland Bauerschmidt, Paul Bourgade, Miika Nikula +1
We study the classical two-dimensional one-component plasma of positively charged point particles, interacting via the Coulomb potential and confined by an external potential.…
Rigidity of Eigenvalues of Generalized Wigner Matrices
Laszlo Erdos, Horng-Tzer Yau, Jun Yin
Consider hermitian or symmetric random matrices with independent entries, where the distribution of the matrix element is given by the probability measure $…
Universality for generalized Wigner matrices with Bernoulli distribution
László Erdos, Horng-Tzer Yau, Jun Yin
The universality for the eigenvalue spacing statistics of generalized Wigner matrices was established in our previous work \cite{EYY} under certain conditions on the probability di…
Bulk universality for generalized Wigner matrices
Laszlo Erdos, Horng-Tzer Yau, Jun Yin
Consider Hermitian or symmetric random matrices where the distribution of the matrix element is given by a probability measure with a subexponentia…
The local relaxation flow approach to universality of the local statistics for random matrices
Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau +1
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…
Universality of Random Matrices and Local Relaxation Flow
Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau
We consider symmetric random matrices where the probability distribution for each matrix element is given by a measure with a subexponential decay. We prove that th…
Bulk Universality for Wigner Matrices
Laszlo Erdos, Sandrine Peche, Jose A. Ramirez +2
We consider Hermitian Wigner random matrices where the probability density for each matrix element is given by the density . We prove that the eig…
Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation
Laszlo Erdos, Jose A. Ramirez, Benjamin Schlein +1
We consider Hermitian random matrices with independent identically distributed entries (Wigner matrices). We assume that the distribution of the entries have a Gaussian…
The Second Order Upper Bound for the Ground Energy of a Bose Gas
Horng-Tzer Yau, Jun Yin
Consider bosons in a finite box interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives…
Wegner estimate and level repulsion for Wigner random matrices
Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau
We consider Hermitian random matrices with independent identically distributed entries (Wigner matrices). The matrices are normalized so that the average spacing betwee…
Feynman graphs and renormalization in quantum diffusion
Laszlo Erdoes, Manfred Salmhofer, Horng-Tzer Yau
We review our proof that in a scaling limit, the time evolution of a quantum particle in a static random environment leads to a diffusion equation. In particular, we discuss the ro…
The ground state energy of a low density Bose gas: a second order upper bound
Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau
Consider bosons in a finite box $Λ= [0,L]^3\subset \bR^3$ interacting via a two-body nonnegative soft potential with fixed and small. We will ta…
Rigorous Derivation of the Gross-Pitaevskii Equation with a Large Interaction Potential
Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau
Consider a system of bosons in three dimensions interacting via a repulsive short range pair potential , where $\bx=(x_1, >..., x_N)$ denotes the positions of…
Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices
László Erdős, Benjamin Schlein, Horng-Tzer Yau
We consider Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order . We st…
Rigorous Derivation of the Gross-Pitaevskii Equation
Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau
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-bo…
Derivation of the Gross-Pitaevskii Equation for the Dynamics of Bose-Einstein Condensate
Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau
Consider a system of bosons in three dimensions interacting via a repulsive short range pair potential , where $\bx=(x_1, >..., x_N)$ denotes the positions of…
Quantum diffusion of the random Schrodinger evolution in the scaling limit II. The recollision diagrams
Laszlo Erdos, Manfred Salmhofer, Horng-Tzer Yau
We consider random Schrödinger equations on $\bR^d$ for with a homogeneous Anderson-Poisson type random potential. Denote by the coupling constant and the soluti…
Quantum diffusion of the random Schrodinger evolution in the scaling limit
Laszlo Erdos, Manfred Salmhofer, Horng-Tzer Yau
We consider random Schrödinger equations on $\bR^d$ for with a homogeneous Anderson-Poisson type random potential. Denote by the coupling constant and the soluti…
Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems
Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau
We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of th…