Related papers: A Dynamic Programming Approach to the Parisi Funct…
The understanding of thermodynamic glass transition has been hindered by the lack of proper models beyond mean-field theories. Here, we propose a three-dimensional lattice glass model on a simple cubic lattice that exhibits the typical…
The main goal of this paper is to apply the machinery of variational analysis and generalized differentiation to study infinite horizon stochastic dynamic programming (DP) with discrete time in the Banach space setting without convexity…
We prove upper and lower bounds on the free energy in the Sherrington-Kirkpatrick model with multidimensional (e.g., Heisenberg) spins in terms of the variational inequalities based on the corresponding Parisi functional. We employ the…
We conjecture that the Parisi functional in the SK model is convex in the functional order parameter and prove a partial result that shows the convexity along one-sided directions. A consequence of this result is log-convexity of L_1 norm…
We focus on spherical spin glasses whose Parisi distribution has support of the form $[0,q]$. For such models we construct paths from the origin to the sphere which consistently remain close to the ground-state energy on the sphere of…
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…
The Parisi formula for the free energy of the Sherrington-Kirkpatrick model is completed to a closed-form generating functional. We first find an integral representation for a solution of the Parisi differential equation and represent the…
The Parisi formula for the free energy in the spherical models with mixed even p-spin interactions was proven in Michel Talagrand [16]. In this paper we study the general mixed p-spin spherical models including p-spin interactions for odd…
We propose an alternative theory for the relaxation of density fluctuations in glass-forming fluids. We derive an equation of motion for the density correlation function which is local in time and is similar in spirit to the equation of…
We study efficient optimization of the Hamiltonians of multi-species spherical spin glasses. Our results characterize the maximum value attained by algorithms that are suitably Lipschitz with respect to the disorder through a variational…
This paper studies the dynamic programming principle for general convex stochastic optimization problems introduced by Rockafellar and Wets in [30]. We extend the applicability of the theory by relaxing compactness and boundedness…
We analyze the full replica symmetry breaking (full--RSB) free energy functional for the Ising spin glass on a random regular graph proposed by the author in \cite{MyPaper}. We prove that the full--RSB formulation provides an improvement…
Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…
We present a critical analysis of the Sompolinsky theory of equilibrium dynamics. By using the spherical $2+p$ spin glass model we test the asymptotic static limit of the Sompolinsky solution showing that it fails to yield a…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
I discuss results from numerical simulations of finite dimensional spin glass models, and show that they show all signatures of a mean field like behavior, basically coinciding with the one of the Parisi solution. I discuss the Binder…
The Parisi solution of the mean-field spin glass has been widely accepted and celebrated. Its marginal stability in 3d and its complexity however raised the question of its relevance to real spin glasses. This paper gives a short overview…
In the study of disordered models like spin glasses the key object of interest is the rugged energy hypersurface defined in configuration space. The statistical mechanics calculation of the Gibbs-Boltzmann Partition Function gives the…
We develop a systematic expansion method of physical quantities for the SK model and the finite-dimensional $\pm J$ model of spin glasses in non-equilibrium states. The dynamical probability distribution function is derived from the master…
The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into the statistical mechanics of systems with highly diversified collections of competing low energy states. The goal of this summary is to present some…