The dynamics of one-parameter diagonal group actions on finite volume homogeneous spaces has a partially hyperbolic feature. In this paper we extend the Livsic-type result to these possibly noncompact and nonaccessible systems. We also prove central limit theorem for Birkhoff averages points horospherical orbit. allows us show that variance is nonzero provided test function mean with respect an...

We consider in this paper random batch particle methods for efficiently solving the homogeneous Landau equation plasma physics. The are stochastic variations of proposed by Carrillo et al. [J. Comput. Phys.: X 7: 100066, 2020] using strategy. collisions only take place inside small but randomly selected batches so that computational cost is reduced to $O(N)$ per time step. Meanwhile, our can pr...