相关论文: Random Energy Model with Compact Distributions

We consider a random matrix model with both pairwise and non-pairwise contracted indices. The partition function of the matrix model is similar to that appearing in some replicated systems with random tensor couplings, such as the p-spin…

We present a variational free-energy formulation for distributionally robust decision-making with ambiguity in the generative model. The formulation, related to a broad range of learning and control frameworks, yields a minimax optimal…

In this paper and in the companion one we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems---the overlap field…

Exponential random graph models have attracted significant research attention over the past decades. These models are maximum-entropy ensembles under the constraints that the expected values of a set of graph observables are equal to given…

A class of conserved models of wealth distributions are studied where wealth (or money) is assumed to be exchanged between a pair of agents in a population like the elastically colliding molecules of a gas exchanging energy. All sorts of…

Magnetizations are introduced to the Generalized Random Energy Model (GREM) and numerical simulations on ac susceptibility is made for direct comparison with experiments in glassy materials. Prominent dynamical natures of spin glasses, {\it…

We discuss the use of a ferromagnetic spin model on a random graph to model granular compaction. A multi-spin interaction is used to capture the competition between local and global satisfaction of constraints characteristic for geometric…

Measurements of a weighted energy density average taken in the vacuum state of a conformal field theory in $1+1$ dimensions are randomly distributed with vanishing expectation value. The probability distribution is computed in closed form…

In the last five decades, mean-field neural-networks have played a crucial role in modelling associative memories and, in particular, the Hopfield model has been extensively studied using tools borrowed from the statistical mechanics of…

The "Money Exchange Model" is a type of agent-based simulation model used to study how wealth distribution and inequality evolve through monetary exchanges between individuals. The primary focus of this model is to identify the limiting…

In a companion paper we developed the generalized TAP approach for general multi-species spherical mixed $p$-spin models. In this paper, we use it to compute the limit of the free energy at any temperature for all pure multi-species…

We consider the spherical limit of multi-matrix models on regular target graphs, for instance single or multiple Potts models, or lattices of arbitrary dimension. We show, to all orders in the low temperature expansion, that when the degree…

A comprehensive review will be given about the rich mathematical structure of mean field spin glass theory, mostly developed, until now, in the frame of the methods of theoretical physics, based on deep physical intuition and hints coming…

We study a statistical model consisting of $N$ basic units which interact with each other by exchanging a physical entity, according to a given microscopic random law, depending on a parameter $\lambda$. We focus on the equilibrium or…

We introduce and analyze free energy landscapes defined by associating to any point inside the sphere a free energy calculated on a thin spherical band around it, using many orthogonal replicas. This allows us to reinterpret, rigorously…

The starting point of the present work is the observation of possible analogies, both at the phenomenological and at the methodological level, between the subcritical transition to turbulence and the glass transition. Having recalled the…

Sample-to-sample free energy fluctuations in spin-glasses display a markedly different behaviour in finite-dimensional and fully-connected models, namely Gaussian vs. non-Gaussian. Spin-glass models defined on various types of random graphs…

We study the semi-discrete directed polymer model introduced by O'Connell-Yor in its stationary regime, based on our previous work on the stationary $q$-totally asymmetric simple exclusion process ($q$-TASEP) using a two-sided $q$-Whittaker…

We show that the Random Energy Model has interesting rejuvenation properties in its frozen phase. Different `susceptibilities' to temperature changes, for the free-energy and for other (`magnetic') observables, can be computed exactly.…

We consider an invariant random matrix model where the standard Gaussian potential is distorted by an additional single pole of order $m$. We compute the average or macroscopic spectral density in the limit of large matrix size, solving the…