Related papers: Random systems and replica field theory
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…
In this paper we study the Random energy model - so called toy model of the spin glass theory - where the underlying distributions are compactly supported. We prove a general theorem on the asymptotics of free energy and obtain formulae in…
This paper is a review containing new original results on the finite order variational sequence and its different representations with emphasis on applications in the theory of variational symmetries and conservation laws in physics.
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…
The stationary points (SPs) of the potential energy landscapes (PELs) of multivariate random potentials (RPs) have found many applications in many areas of Physics, Chemistry and Mathematical Biology. However, there are few reliable methods…
A pedagogical introduction to the cluster-perturbation theory, the variational cluster approximation and to self-energy-functional theory is given. Some standard applications and the relation to dynamical mean-field theory are discussed.
We use a recently proved fluctuation theorem for the currents to develop the response theory of nonequilibrium phenomena. In this framework, expressions for the response coefficients of the currents at arbitrary orders in the thermodynamic…
In these lectures we discuss some elementary concepts in connection with the theory of symmetric spaces applied to ensembles of random matrices. We review how the relationship between random matrix theory and symmetric spaces can be used in…
This paper contains results relating currents and voltages in resistive networks to appropriate random trees or forests in those networks.
This review summarizes Effective Field Theory techniques, which are the modern theoretical tools for exploiting the existence of hierarchies of scale in a physical problem. The general theoretical framework is described, and explicitly…
In these notes we introduce briefly the fundamentals of the replica method in the context of liquid theory and the structural glass problem. In particular, we explain and show its usefulness as a computation framework in the context of the…
The mathematical description of stable particle-like systems appearing in relativistic quantum field theory at large, respectively small scales or non-zero temperatures is discussed.
Often we wish to predict a large number of variables that depend on each other as well as on other observed variables. Structured prediction methods are essentially a combination of classification and graphical modeling, combining the…
We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.
The Boltzmann-Gibbs probability distributions generated by logarithmically correlated random potentials provide a simple yet nontrivial example of disorder-induced multifractal measures. We introduce and discuss two analytically tractable…
This progress report covers recent developments in the area of quantum randomness, which is an extraordinarily interdisciplinary area that belongs not only to physics, but also to philosophy, mathematics, computer science, and technology.…
Quantum fluctuations, through quantum corrections, have the potential to lead to irreversibility in quantum field theory. We consider the virtual ``charge" distribution generated by quantum corrections in the leading log, short range…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
In this paper, we review the history, current state-of-art, and physical applications of the spectral theory of two classes of random functions. One class consists of homogeneous and isotropic random fields defined on a Euclidean space and…
The physics of randomness and regularities for languages (mother tongues) and their lifetimes and family trees and for the second languages are studied in terms of two opposite processes; random multiplicative noise [1], and fragmentation…