MATEMATICAL ANALYSIS OF INFINITE DIMENSIONAL STOCHASTIC MODELS

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We performed this research project on "Mathematical Analysis of Infinite Dimensional Stochastic Models", and obtained the following results.1.Asymptotics of Lyapunov exponent of Anderson model : It is established that the discrete heat equation with space-time white noise potential over the discrete Euclidean space, so salled "Parabolic Anderson model" has a Lyapunov exponent exhibiting the exponential order of the solution, which is independent of initial conditions. Morever we developed asymptotic analysis of the exponent with respect to the coupling constant and obtained precise asymptotic formula.2.Directed Polymers in Random environment : The theory of directed polymers in random environments is still underdeveloping, particularly in low dimensional cases. We established equivalence of local property of the sample path and some decay order of the random partition functions.3.One of co-workers of this project investigated spectrum structure of random Schroedinger operator over line graph and proved "Anderson localization", another one investigated ergodic properties of the shift dynamics associated with fermion random fields. The other one contributed to the rigorous theory of critical phenomena for stochastic statistical mechanics in establishing presice asymptotic order of two point functions in self-avoiding random walk models and related models.