2023/04/11 by Antonin Chodron de Courcel, de Courcel, Antonin Chodron, Matthew Rosenzweig +3 · 4 citations
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Cosmology and Gravitation Theories #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2304.05315
We consider conservative and gradient flows for N-particle Riesz energies with mean-field scaling on the torus \mathbbTd, for d≥ 1, and with thermal noise of McKean-Vlasov type. We prove global well-posedness and relaxation to equilibrium rates for the limiting PDE. Combining these relaxation rates with the modulated free energy of Bresch et al. and recent sharp functional inequalities of the last two named authors for variations of Riesz modulated energies along a transport, we prove uniform-in-time mean-field convergence in the gradient case with a rate which is sharp for the modulated energy pseudo-distance. For gradient dynamics, this completes in the periodic case the range d-2≤ s