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Quantitative propagation of chaos for generalized Kac particle systems. (English) Zbl 1339.60138
Summary: We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac’s model of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising in kinetic economic models. We obtain explicit rates of convergence for the Wasserstein distance between the law of the particles and their limiting law, which are linear in time and depend in a mild polynomial manner on the number of particles. The proof is based on a novel coupling between the particle system and a suitable system of nonindependent nonlinear processes, as well as on recent sharp estimates for empirical measures.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C22 Interacting particle systems in time-dependent statistical mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
91B70 Stochastic models in economics
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