Seminar Analysis and Mathematical Physics: Peter Pickl (LMU München)

Derivation of the Vlasov equation: Different types of convergence

Abstract: The derivation of effective descriptions from microscopic      dynamics is a very vivid area in mathematical physics. In the talk I      will discuss a system of many particles with Newtonian time evolution      that are subject to interaction. It is well known that in the weak      coupling limit this system converges, under smoothness assumption on      the interaction force, to a solution of the Vlasov equation.    Weakening the types of convergence (convergence for all initial      conditions -> convergence in probability -> convergence in      distribution) the smoothness condition on the interaction can be      generalized. In the talk I will present recent results in this      direction and explain, which types of convergence hold/do not hold      under the different assumptions on the interaction force.

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