University of Cambridge > Talks.cam > Geometric Analysis & Partial Differential Equations seminar > Long time behaviour of kinetic Fokker-Planck models for Elo Chess ranking and when applying hypocoercivity methods can be really hard.

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Long time behaviour of kinetic Fokker-Planck models for Elo Chess ranking and when applying hypocoercivity methods can be really hard.

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If you have a question about this talk, please contact Dr Greg Taujanskas .

This is based on a joint work with Bertram During and Marie-Therese Wolfram about the existence of steady states for a non-linear kinetic Fokker-Planck type equation modelling the evolution of Elo chess ranks. We imagine players with and intrinsic strength, rho, which changes according to random fluctuations and a learning process through playing in matches and a ranking, R, which is updated as the players play matches. This equation has a similar structure to kinetic McKean-Vlasov processes. In this talk I will focus on the analysis of related linear kinetic Fokker-Planck equations and contrast it to the original kinetic Fokker-Planck equation in gas dynamics. We look at applying the techniques of hypocoercivity, where there are several difficulties related to the weak confinement, weak mixing, and open system nature of the equation.

This talk is part of the Geometric Analysis & Partial Differential Equations seminar series.

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