BOLTZMANN-LIKE KINETIC-MODELS AND BOLTZMANN MAPS

This work shows how Boltzmann maps can be used in the study of a class of kinetic models formally similar to those recently proposed in popu lation dynamics. Boltzmann maps are nonlinear, discrete, doubly-stocha stic processes which have been introduced in statistical physics for t he description of nonequilibrium phenomena. The key feature of Boltzma nn maps is that they increase the entropy, when applied to nonstationa ry states, if their interaction operators have a spectral gap. This fa ct can be used to analyse the asymptotic behaviour of the relevant dyn amics. In particular, in some circumstances we can prove that stationa ry states exist, are unique, and stable. Moreover, we can supplement t hese results with theorems on the global convergence of the dynamics t o such stationary states.