arXiv subjects
Publications and source records attributed to Baige Zhou.
For the speed-change Kawasaki dynamics, we study the weak convergence of its quadratic field, and derive the equilibrium fluctuation. This extends the result of Gon{\c{c}}alves and Jara [ALEA, Lat. Am. J. Probab. Math. Stat. 16, 605-632 (2019)] to the non-gradient case.
We present a stochastic Justh-Krishnaprasad flocking model and study the phase transition of the Vlasov-McKean-Fokker-Planck (VMFP) equation, which can be obtained in the mean-field limit. To describe the alignment, we use order parameters in terms of the distribution function of the kinetic model. For the constant noise case, we study the well-posedness of the VMFP equation on the torus. Based on regularity, we show that the phenomenon of phase transition is only related to the ratio between the strengths of noise and coupling. In particular, for the low-noise case, we derive an exponential convergence to the von-Mises type equilibrium, which shows a strong evidence for the nematic alignment. The multiplicative noise is also studied to obtain a non-symmetric equilibrium with two different peaks on the torus.