7 papers
Atomically-sharp magnetic soliton in the square-net lattice EuRhAlSi
Kevin Allen, Juba Bouaziz, Yichen Zhang +17
Topological spin textures are hallmark manifestations of competing interactions in magnetic matter. Their effective description by nonlinear field theories reflects an energetic fr…
Propagation of chaos for the Landau equation via microcanonical binary collisions
Kai Du
We develop a fully constructive, conservative, and collision-level realization of Kac's program for the spatially homogeneous Landau equation across the full interaction range, inc…
Optimal control of SDEs with merely measurable drift: an HJB approach
Kai Du, Qingmeng Wei
We investigate an optimal control problem for a diffusion whose drift and running cost are merely measurable in the state variable. Such low regularity rules out the use of Pontrya…
Empirical approximation to invariant measures of mean-field Langevin dynamics
Wenjing Cao, Kai Du
This paper is concerned with the approximation to invariant measures for Langevin dynamics of McKean--Vlasov type. Under dissipativity and Lipschitz conditions, we prove that the e…
Particle approximation for a conditional McKean--Vlasov stochastic differential equation
Kai Du, Yunzhang Li, Yuyang Ye
In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability…
Self-interacting approximation to McKean-Vlasov long-time limit: a Markov chain Monte Carlo method
Kai Du, Zhenjie Ren, Florin Suciu +1
For a certain class of McKean-Vlasov processes, we introduce proxy processes that substitute the mean-field interaction with self-interaction, employing a weighted occupation measu…
Empirical approximation to invariant measures of non-degenerate McKean-Vlasov dynamics
Wenjing Cao, Kai Du
This paper studies the approximation of invariant measures of McKean-Vlasov dynamics with non-degenerate additive noise. While prior findings necessitated a strong monotonicity con…