3 papers
cs.AI2026
A Formalization of the Mean-Field Derivation of the Vlasov Equation
Joseph K. Miller
We formalize a research result in the Lean 4 proof assistant by having a mathematician direct an AI system, and frame the activity as a formalization game. The objective is to turn…
math.AP2022
A rigorous derivation of the Hamiltonian structure for the Vlasov equation
Joseph K. Miller, Andrea R. Nahmod, Nataša Pavlović +2
We consider the Vlasov equation in any spatial dimension, which has long been known to be an infinite-dimensional Hamiltonian system whose bracket structure is of Lie-Poisson type.…
math.AP2021
A Rigorous Derivation of a Boltzmann System for a Mixture of Hard-Sphere Gases
Ioakeim Ampatzoglou, Joseph K. Miller, Nataša Pavlović
In this paper, we rigorously derive a Boltzmann equation for mixtures from the many body dynamics of two types of hard sphere gases. We prove that the microscopic dynamics of two g…