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We study the asymptotic behavior, in the zero-noise limit, of solutions to Schrödingers functional equations and that of h-path processes, and give a new proof of the existence of the minimizer of Monge's problem with a quadratic cost.Partially supported by the Grant-in-Aid for Scientific Research, No. 15340047 and 15340051, JSPS

Monge’s problem with a quadratic cost by the zero-noise limit of h-path processes