Large N limit of the Langevin dynamics for the spin O(N) model
Event details
| Date | 27.02.2026 |
| Hour | 15:30 › 16:30 |
| Speaker | Prof. Wenjie Ye |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Abstract: In this paper, we prove that the large N limit of the Langevin dynamics for the spin O(N) model is given by a mean-field stochastic differential equation (SDE) in both finite and infinite volumes. We establish uniform in N bounds for the dynamics, which enable us to demonstrate convergence to the mean-field SDE with polynomial interactions. Furthermore, the mean-field SDE is shown to be globally well-posed for suitable initial distributions. We also prove the existence of stationary measures for the mean-field SDE. For small inverse temperatures, we characterize the large N limit of the spin O(N) model through stationary coupling. Additionally, we establish the uniqueness of the stationary measure for the mean-field SDE. This research is a joint work with Rongchan Zhu.
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