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We study the connection between a system of many independent Brownian particles on one hand and the deterministic diffusion equation on the other.
Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen
A. Einstein · 1905
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Sanov property, generalized I-projection and a conditional limit theorem
I. Csiszár · 1984
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Large deviations
J. D. Deuschel and D. W. Stroock · 1989
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Large deviations from the hydrodynamical limit for a system of independent Brownian particles
C. Kipnis and S. Olla · 1990
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Mathematical methods for hydrodynamic limits
A. De Masi and E. Presutti · 1992
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Measure Theory and Fine Properties of Functions
L. C. Evans and R. F. Gariepy · 1992
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An Introduction to Γ \Gamma -Convergence
G. Dal Maso · 1993
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Free energy and the Fokker-Planck equation
R. Jordan, D. Kinderlehrer, and F. Otto · 1997
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A convexity principle for interacting gases
R. J. McCann · 1997
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Theory of anomalous chemical transport in random fracture networks
B. Berkowitz and H. Scher · 1998
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The variational formulation of the Fokker-Planck Equation
R. Jordan, D. Kinderlehrer, and F. Otto · 1998
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Lubrication approximation with prescribed nonzero contact angle
F. Otto · 1998
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Scaling limits of interacting particle systems
C. Kipnis and C. Landim · 1999
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Anomalous transport in laboratory-scale, heterogeneous porous media
B. Berkowitz, H. Scher, and S.E. Silliman · 2000
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F. den Hollander · 2000
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Variational formulations for Vlasov-Poisson-Fokker-Planck systems
C. Huang and R. Jordan · 2000
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Subdiffusion and the cage effect studied near the colloidal glass transition
E. R. Weeks and D. A. Weitz · 2002
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A diffuse-interface approach to Hele-Shaw flow
K. Glasner · 2003
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Topics in Optimal Transportation
C. Villani · 2003
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Gradient Flows in Metric Spaces and in the Space of Probability Measures
L. Ambrosio, N. Gigli, and G. Savaré · 2005
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Contractions in the 2-Wasserstein length space and thermalization of granular media
J. A. Carrillo, R. J. McCann, and C. Villani · 2006
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Variational formulation for the lubrication approximation of the Hele-Shaw flow
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