Abstract
We consider a large number of particles diffusing on a circle interacting through a drift resulting from the gradient of a pair potential whose support is of the order of the interparticle distance. We derive a nonlinear bulk diffusion equation for the density of the particle distribution on the circle. The diffusion coefficient is determined as a function of density in terms of standard thermodynamical objects.
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Communicated by J.L. Lebowitz
This research was supported by a grant from the National Science Foundation DMS-89-01682
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Varadhan, S.R.S. Scaling limits for interacting diffusions. Commun.Math. Phys. 135, 313–353 (1991). https://doi.org/10.1007/BF02098046
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DOI: https://doi.org/10.1007/BF02098046