Gibbs measures, as used in Statistical Mechanics, have a definition that is remarkably similar to the definition ofg-measures, used in dynamical systems. For both types of measures the continuity... Show moreGibbs measures, as used in Statistical Mechanics, have a definition that is remarkably similar to the definition ofg-measures, used in dynamical systems. For both types of measures the continuity of conditional probabilities play a central role.In this thesis we give necessary and sufficient conditions for when a g-measure is a Gibbs measure. We relate this result to well known uniqueness conditions and briefly consider the related question: when is a g-measure reversible.Subsequently we consider an application in information theory by considering whether one-sided models can be used for two-sided modeling.Finally, we apply a technique called measure disintegration to give very general conditions for when the conditional probabilities of factors of Markov processesare g-measures and factors of Gibbs measure are Gibbs measures. Show less
In this work we describe three methods to improve the performance of Quantum Field Theory calculations. First, we simplify large expressions to speed up numerical integrations. Second, we design... Show moreIn this work we describe three methods to improve the performance of Quantum Field Theory calculations. First, we simplify large expressions to speed up numerical integrations. Second, we design Forcer, a program for the reduction of four-loop massless propagator integrals. Third, we extend the R* method to quickly compute the poles of Feynman integrals. With these methods, we compute several four-loop splitting functions and the five-loop beta function for Yang-Mills theory with fermions. Show less
