Summary
It is remarked that for Brownian particles interacting with a smooth repulsive pair potential the nonlinear diffusion equation which S. Varadhan has derived under an entropy bound for initial densities is valied whatever initial distribution they start with.
References
Lu, S.: Hydrodynamic scaling limits starting with deterministic initial configurations (Preprint)
Olla, Varadhan, S.R.S.: Scaling limit for interacting Ornstein-Uhlenbeck processes. Commun. Math. Phys.135, 355–378 (1991)
Suzuki, Y., Uchiyama, K.: Hydrodynamic limit for a spin system on a multidimensional lattice. Probab. Theory Relat. Fields95, 47–74 (1993)
Varadhan, S.R.S.: Scaling limits for interacting diffusions. Commun. Math. Phys.135, 313–353 (1991)
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Research partially supported by Japan Society for the Promotion of Science
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Uchiyama, K. Scaling limits of interacting diffusions with arbitrary initial distributions. Probab. Th. Rel. Fields 99, 97–110 (1994). https://doi.org/10.1007/BF01199591
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DOI: https://doi.org/10.1007/BF01199591
Mathematics Subject Classification (1991)
- 60K35