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Quantitative estimates of propagation of chaos for stochastic systems with $$W^{-1,\infty }$$ W - 1 , ∞ kernels
- Source :
- Inventiones mathematicae. 214:523-591
- Publication Year :
- 2018
- Publisher :
- Springer Science and Business Media LLC, 2018.
-
Abstract
- We derive quantitative estimates proving the propagation of chaos for large stochastic systems of interacting particles. We obtain explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit. We have to develop for this new laws of large numbers at the exponential scale. But our result only requires very weak regularity on the interaction kernel in the negative Sobolev space $\dot W^{-1,\infty}$, thus including the Biot-Savart law and the point vortices dynamics for the 2d incompressible Navier-Stokes.<br />59 pages
- Subjects :
- Kullback–Leibler divergence
General Mathematics
010102 general mathematics
Mathematical analysis
FOS: Physical sciences
Scale (descriptive set theory)
Mathematical Physics (math-ph)
01 natural sciences
Exponential function
Physics::Fluid Dynamics
010101 applied mathematics
Sobolev space
Mathematics - Analysis of PDEs
Law of large numbers
Kernel (statistics)
FOS: Mathematics
Compressibility
Limit (mathematics)
0101 mathematics
Mathematical Physics
Analysis of PDEs (math.AP)
Mathematics
Subjects
Details
- ISSN :
- 14321297 and 00209910
- Volume :
- 214
- Database :
- OpenAIRE
- Journal :
- Inventiones mathematicae
- Accession number :
- edsair.doi.dedup.....a407e85be9b55973f2a271c877114dd7