The asymptotic Rényi distances are explicitly defined and rigorously studied for a convenient class of Gibbs random fields, which are introduced as a natural infinite-dimensional generalization of exponential distributions.
We study the zero-temperature limit for Gibbs measures associated to Frenkel–Kontorova models on . We prove that equilibrium states concentrate on configurations of minimal energy, and, in addition, must satisfy a variational principle involving metric entropy and Lyapunov exponents, a bit like in the Ruelle–Pesin inequality. Then we transpose the result to certain continuous-time stationary stochastic processes associated to the viscous Hamilton–Jacobi equation. As the viscosity vanishes, the...
We consider the following problem: where Φ: Ω ⊂ → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.
We review the appearance of the braid group in statistical physics. In particular, we explain its relevance to the anyon model of fractional statistics and conformal field theory.