Related papers: TAP equations are repulsive
We describe the fluctuations of the overlap between two replicas in the 2-spin spherical SK model about its limiting value in the low temperature phase. We show that the fluctuations are of order $N^{-1/3}$ and are given by a simple,…
We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical…
Entropy stable schemes replicate an entropy inequality at the semi-discrete level. These schemes rely on an algebraic summation-by-parts (SBP) structure and a technique referred to as flux differencing. We provide simple and efficient…
Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…
We study the temperature structure of the naive TAP equations by mean of a recursion algorithm. The problem of the chaos in temperature is addressed using the notion of the temperature evolution of equilibrium states. The lowest free energy…
A basic problem in operator theory is to estimate how a small perturbation effects the eigenspaces of a self-adjoint compact operator. In this paper, we prove upper bounds for the subspace distance, taylored for structured random…
Macroscopic quantum superpositions are widely believed to be unobservable because large systems cannot be perfectly isolated from their environments. Here, we show that even under perfect isolation, intrinsic unitary dynamics with the…
A perturbation decaying to 0 at infinity and not too irregular at 0 introduces at most a discrete set of eigenvalues into the spectral gaps of a one-dimensional Dirac operator on the half-line. We show that the number of these eigenvalues…
In this article, we consider a class of finite rank perturbations of Toeplitz operators that have simple eigenvalues on the unit circle. Under a suitable assumption on the behavior of the essential spectrum, we show that such operators are…
For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here ``eigenvalue''…
The linear response to temperature changes is derived for systems with overdamped stochastic dynamics. Holding both in transient and steady state conditions, the results allow to compute nonequilibrium thermal susceptibilities from…
We compute the thermodynamic properties of the 3-satisfiability problem in the infinite connectivity limit. In this limit the computations can be strongly simplified and the thermodynamical properties can be obtained with an high accuracy.…
We provide a new perspective on the pseudogap physics for attractive fermions as described by the three-dimensional Hubbard model. The pseudogap in the single-particle spectral function, which occurs for temperatures above the critical…
Aim of the paper is to provide a method to analyze the behavior of $T$-periodic solutions $x_\eps, \eps>0$, of a perturbed planar Hamiltonian system near a cycle $x_0$, of smallest period $T$, of the unperturbed system. The perturbation is…
We present a comprehensive treatment of relative oscillation theory for finite Jacobi matrices. We show that the difference of the number of eigenvalues of two Jacobi matrices in an interval equals the number of weighted sign-changes of the…
Engineered systems naturally experience large disturbances that can disrupt desired operation because the system may fail to recover to a stable equilibrium point. It is valuable to determine the mechanism of instability when the system is…
Two general upper bounds on the topological entropy of nonlinear time-varying systems are established: one using the matrix measure of the system Jacobian, the other using the largest real part of the eigenvalues of the Jacobian matrix with…
We study estimation in the linear model $y=A\beta^\star+\epsilon$, in a Bayesian setting where $\beta^\star$ has an entrywise i.i.d. prior and the design $A$ is rotationally-invariant in law. In the large system limit as dimension and…
We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddle-node bifurcation. It was previously shown that for a parameter set of positive Lebesgue density at the bifurcation, the maps possess…
A new Jacobian approximation is developed for use in quasi-Newton methods for solving systems of nonlinear equations. The new hypersecant Jacobian approximation is intended for the special case where the evaluation of the functions whose…