By Tomasz Komorowski
The current quantity comprises the main complex theories at the martingale method of primary restrict theorems. utilizing the time symmetry homes of the Markov techniques, the publication develops the innovations that let us to accommodate endless dimensional versions that seem in statistical mechanics and engineering (interacting particle platforms, homogenization in random environments, and diffusion in turbulent flows, to say quite a few applications). the 1st half features a specific exposition of the strategy, and will be used as a textual content for graduate classes. the second one issues program to exclusion strategies, during which the duality tools are absolutely exploited. The 3rd half is set the homogenization of diffusions in random fields, together with passive tracers in turbulent flows (including the superdiffusive behavior).
There are not any different books within the mathematical literature that care for this type of method of the matter of the primary restrict theorem. accordingly, this quantity meets the call for for a monograph in this strong procedure, now commonly used in lots of parts of likelihood and mathematical physics. The publication additionally covers the connections with and alertness to hydrodynamic limits and homogenization concept, so in addition to likelihood researchers it is going to even be of curiosity additionally to mathematical physicists and analysts.
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