Abstract: Composite media plays an important role in the real world, and one of the central problems is to understand the diffusion processes in a long cylinder with high conductivity concentrated on a thin layer near the boundary. Since the layer is thin and the
microscopic structure is very complicated, the amount of the computation exceeds the capacity of a computer. The technique which we
use to overcome this difficulty is the homogenization; namely, we consider an ideal model and show that the stochastic process in this
ideal space well approximates the ``real one". Mathematically, this amounts to prove the weak convergence of the Wiener measures
associated to the ``real one" to the Wiener measure on the ideal space. The main two steps in our argumentation are: first, to
establish the convergence of the heat-semigroups which govern the dynamics to the heat-semigroup on the ideal space; and secondly, to show the tightness of the associated Wiener measures. The first step identifies the limit - if it exists - and the second step verifies the existence of the limit, and combing those two results, we deduce the weak convergence of the Wiener measures.

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If you are interested in giving a talk, please contact Dr. Zhaohu Nie, the current Colloquium Coordinator.