Uniform-in-Time Estimates on the Size of Chaos for Interacting Particle Systems
Copyright policy )Uniform-in-Time Estimates on the Size of Chaos for Interacting Particle Systems
For any weakly interacting particle system with bounded kernel, we give uniform-in-time estimates of the $L^2$ norm of correlation functions, provided that the diffusion coefficient is large enough. When the condition on the kernels is more restrictive, we can remove the dependence of the lower bound for diffusion coefficient on the initial data and estimate the size of chaos in a weaker sense. Based on these estimates, we may study fluctuation around the mean-field limit.
25 pages
- Fudan University China (People's Republic of)
interacting particle systems, Functional limit theorems; invariance principles, Probability (math.PR), central limit theorem, 35Q70, 35Q83, 60F17, 60H10, PDEs in connection with mechanics of particles and systems of particles, FOS: Physical sciences, Mathematical Physics (math-ph), long-time behavior, Stochastic ordinary differential equations (aspects of stochastic analysis), Mathematics - Analysis of PDEs, size of chaos, FOS: Mathematics, Vlasov equations, Mathematical Physics, Mathematics - Probability, Analysis of PDEs (math.AP)
interacting particle systems, Functional limit theorems; invariance principles, Probability (math.PR), central limit theorem, 35Q70, 35Q83, 60F17, 60H10, PDEs in connection with mechanics of particles and systems of particles, FOS: Physical sciences, Mathematical Physics (math-ph), long-time behavior, Stochastic ordinary differential equations (aspects of stochastic analysis), Mathematics - Analysis of PDEs, size of chaos, FOS: Mathematics, Vlasov equations, Mathematical Physics, Mathematics - Probability, Analysis of PDEs (math.AP)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!