Bäcklund transformation for the BC-type Toda lattice.
Bernouilli and Gibbs Probabilities of Subgroups of {0, 1} s.
Bethe Ansatz and the geography of rigged strings
We demonstrate the way in which composition of two famous combinatorial bijections, of Robinson-Schensted and Kerov-Kirillov-Reshetikhin, applied to the Heisenberg model of magnetic ring with spin 1/2, defines the geography of rigged strings (which label exact eigenfunctions of the Bethe Ansatz) on the classical configuration space (the set of all positions of the system of r reversed spins). We point out that each l-string originates, in the language of this bijection, from an island of l consecutive...
Bethe ansatz, inverse scattering transform and tropical Riemann theta function in a periodic soliton cellular automaton for .
Bethe ansatz solutions of the Bose-Hubbard dimer.
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...