Mathematical Sciences: Markov Processes

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The principal investigator will study the problem of hydrodynamical or macroscopic limiting bahaviour of large systems under suitable scaling of space and time. This problem is important both in the classical as well as the stochastic context. The principal investigator expects to use techniques from large deviations theory (spatial as well as temporal) to study this phenomenon. In the last few years the principal investigator with others has developed techniques that make effective use of Dirichlet forms in ths context. These techniques will be modified to cover large classes of such problems. Solutions of these problems will impact both probability and mathematical physics.