Abstract
The phenomenon propagation of chaos describes a cloud of identical particles which behave asymptotically, as their number tends to infinity, independently and identically according to a limiting distribution. We introduce a coherent definition in terms of relative entropy in the tradition of statistical mechanics.
Investigating the inverse problem raised in Nagasawa [38] means to start with certain limiting distributions and to furnish them with microscopical systems which perform propagation of chaos.
The considered limiting distributions are diffusion processes arising from the statistically relevant situation of given particle dynamics and prescribed marginal distributions at initial and final time. They actually describe a wide range of observed phenomena to which the fundamental hypothesis of statistical mechanics applies. We will give an application to diffusions related to wave functions in quantum mechanics.
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Aebi, R. (1995). Propagation of Chaos — The Inverse Problem. In: Bolthausen, E., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications. Progress in Probability, vol 36. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7026-9_1
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