A strong limit theorem is proved for a version of the well-known Kac-Zwanzig model, in which a 'distinguished' particle is coupled to a bath of N free particles through linear springs with random stiffness. It is shown that the evolution of the distinguished particle, albeit generated from a deterministic set of dynamical equations, converges pathwise towards the solution of an integro-differential equation with a random noise term. Both the canonical and microcanonical ensembles are considered.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics