Un algorithme dérivé de l'algorithme de Metropolis

Abstract

Statistical physics and stochastic modelling in economic sciences share the same mathematical bases given by the Gibbs distribution, but system characteristics are different. For instance, an economic system can be described by a Bose–Einstein statistics with few non-degenerate states and an infinitesimal “temperature”; under such conditions, the approximation of the most probable configuration is invalid. Therefore, the calculus of the exact solution needs using a Metropolis algorithm, which estimates a Gibbs distribution. This paper presents a much more efficient algorithm. For small systems, the exact distribution on the canonical set can be computed, and then this distribution is compared to the solutions of the old and new algorithms.