Related papers: Random systems and replica field theory
This is a (long) survey about applications of percolation theory in equilibrium statistical mechanics. The chapters are as follows: 1. Introduction 2. Equilibrium phases 3. Some models 4. Coupling and stochastic domination 5. Percolation 6.…
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
Random Phase Approximation (RPA) is the theory most commonly used to describe the excitations of many-body systems. In this article, the secular equations of the theory are obtained by using three different approaches: the equation of…
Contents: A. Introduction B. High Temperature Expansions for the Ising Model C. Characteristic Functions and Cumulants D. The One Dimensional Chain E. Directed Paths and the Transfer Matrix F. Moments of the Correlation Function G. The…
This PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematical studies of lattice systems in statistical and quantum…
This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory. This review also attempts to provide a physical context in which to interpret these results by…
Prepared for the Quantum Field Theory section of the Encyclopedia of Mathematical Physics, Elsevier, 2006. A brief introduction to the methodology and techniques of perturbative relativistic quantum field theory is presented.
Contents: 1. Pomeron physics 2. Multiplicities 3. Single-particle distributions 4. Correlations and fluctuations 5. Special final states and interaction mechanisms 6. Cosmic rays and forward detectors
The complicated processes in the medium (decays, reactions and $n\bar{n}$ conversion) involving final state absorption are considered. The calculations in the framework of field and phenomenological approaches are compared. The reasons for…
This text provides a practical introduction to randomness and data analysis, in particular in the context of computer simulations. At the beginning, the most basics concepts of probability are given, in particular discrete and continuous…
This article is preface to the SIGMA special issue "Tensor Models, Formalism and Applications", http://www.emis.de/journals/SIGMA/Tensor_Models.html. The issue is a collection of eight excellent, up to date reviews on random tensor models.…
Sec I - Introduction Sec II - Equilibrium properties: generalities and methodology Sec III - Equilibrium properties: some important quantities Sec IV - Dynamical properties: heuristic approach Sec V - Dynamical properties: stochastic…
A fairly non-technical introduction to and survey of supersymmetry phenomenology with pedagogical emphasis, including exercises. Suitable for both theorists and experimentalists. The manuscript appeared as a Springer-Verlag monograph in…
Random Wavelet Series form a class of random processes with multifractal properties. We give three applications of this construction. First, we synthesize a random function having any given spectrum of singularities satisfying some…
The equations for phase transitions temperatures, order parameters and critical concentrations of components have been derived for mixed ferroelectrics. The electric dipoles randomly distributed over the system were considered as a random…
This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…
Contents: 1. Introduction 2. Bosonic propagators and random paths 3. Random surfaces and strings 4. Matrix models and two-dimensional quantum gravity 5. The mystery of $c > 1$ 6. Euclidean quantum gravity in $d > 2$ 7. Discussion
We present an overview of selected topics in random permutations and random partitions highlighting analogies with random matrix theory.
Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their…
An infinite range spin glass like model for granular systems is introduced and studied through the replica mean field formalism. Equilibrium, density dependent properties under vibration and gravity are obtained.