Bethe ansatz solutions to quasi exactly solvable difference equations.
Bipartite mean field spin systems. Existence and solution.
Boltzmann Asymptotics with Diffuse Reflection Boundary Conditions.
Boltzmann-Gibbs entropy: Axiomatic characterization and application.
Boundary value problems for the ellipsoidal statistical equation.
Bounding a random environment bounding a random environment for two-dimensional edge-reinforced random walk.
Bounding the partition function of spin-systems.
Bounds on the zeros of a renormalization group fixed point.
Branching processes, and random-cluster measures on trees
Random-cluster measures on infinite regular trees are studied in conjunction with a general type of ‘boundary condition’, namely an equivalence relation on the set of infinite paths of the tree. The uniqueness and non-uniqueness of random-cluster measures are explored for certain classes of equivalence relations. In proving uniqueness, the following problem concerning branching processes is encountered and answered. Consider bond percolation on the family-tree of a branching process. What is the...
Brownian particles with electrostatic repulsion on the circle : Dyson’s model for unitary random matrices revisited
The brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices is interpreted as a system of interacting brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). We prove that a limiting...
Brownian particles with electrostatic repulsion on the circle: Dyson's model for unitary random matrices revisited
The Brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices N x N is interpreted as a system of N interacting Brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles N goes to infinity (through the empirical measure process). We prove...
Cahn-Hilliard equation with terms of lower order and non-constant mobility.
C*-algebraic generalization of relative entropy and entropy
Canonical distributions and phase transitions
Entropy maximization subject to known expected values is extended to the case where the random variables involved may take on positive infinite values. As a result, an arbitrary probability distribution on a finite set may be realized as a canonical distribution. The Rényi entropy of the distribution arises as a natural by-product of this realization. Starting with the uniform distributionon a proper subset of a set, the canonical distribution of equilibriumstatistical mechanics may be used to exhibit...
Capacity bounds for the CDMA system and a neural network: a moderate deviations approach
We study two systems that are based on sums of weakly dependent Bernoulli random variables that take values ± 1 with equal probabilities. We show that already one step of the so-called soft decision parallel interference cancellation, used in the third generation of mobile telecommunication CDMA, is able to considerably increase the number of users such a system can host. We also consider a variant of the well-known Hopfield model of neural networks. We show that this variant proposed by Amari...
Cascaded Channels and the Equivocation Inequality.
Cavity method in the spherical SK model
We develop a cavity method for the spherical Sherrington–Kirkpatrick model at high temperature and small external field. As one application we compute the limit of the covariance matrix for fluctuations of the overlap and magnetization.
Central limit theorems for the Potts model.
Chaotic hypothesis and universal large deviations properties.
Choosing Hydrodynamic Fields
Continuum mechanics (e.g., hydrodynamics, elasticity theory) is based on the assumption that a small set of fields provides a closed description on large space and time scales. Conditions governing the choice for these fields are discussed in the context of granular fluids and multi-component fluids. In the first case, the relevance of temperature or energy as a hydrodynamic field is justified. For mixtures, the use of a total temperature and single...