Mathematical Sciences: Random Fields

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The main researcher for this project will be a post-doc to the principal investigator. The researcher will continue his work on the random fields. Infinite dimensional probability spaces provide excellent models in the study of Eucleadian quantum field theory and equilibrium statistical mechanics. The probability spaces providing the models have parameters that correspond to temperature, momentum cutoff and coupling constants etc.. Various phenomena such as phase transition, symmetry breaking and consequences of renormalization can be predicted by varying these perameters. Except in very simple situations, the proofs of these predictions are difficult to accomplish rigorously. The researcher will try to attack some of these intriguing problems via the use of techniques from nonhomogeneous Gaussian processes associated with the free Markov field.