Numerical Analysis Seminars: Time-evolution of Probability Measures on Collision Trees -- a Tool for Micro-macro Transitions
20 January 2012 14:00 in CG83
A method is presented to show the validity of continuum description for the deterministic dynamics of many interacting particles with random initial data. Considering a simplified case of hard-spehere dynamics, where particles are removed after the first collision, we characterize the many particle flow by collision trees which encode possible collisions. The convergence of the many-particle dynamics to the Boltzmann dynamics is achieved via the convergence of associated probability measures on collision trees. These probability measures satisfy nonlinear Kolmogorov equations, which are crucial in the convergence proof. We also outline how these methods are relevant for full hard-sphere dynamics and its relation to the Boltzmann equation. Joint work with Florian Theil.
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