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Abstract: Dynamics of a system that performs a large fluctuation to a given state isessentially deterministic: the distribution of fluctuational paths peakssharply at a certain optimal path along which the system is most likely tomove. For the general case of a system driven by colored Gaussian noise, weprovide a formulation of the variational problem for optimal paths. We alsoconsider the prehistory problem, which makes it possible to analyze the shapeof the distribution of fluctuational paths that arrive at a given state. Weobtain, and solve in the limiting case, a set of linear equations for thecharacteristic width of this distribution.



Author: M.I. Dykman, V.N. Smelyanskiy

Source: https://arxiv.org/



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