Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
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Introduces bundles as morphisms in a category of finite probability schemes to give functorial conditional expectation, conditional independence via fiber products, Markov chains from pairwise schemes, and identifications with relative traces and Frobenius reciprocity.
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Weyl asymptotic formulas in the nilpotent Lie group setting
Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
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Bundles of Probability Schemes
Introduces bundles as morphisms in a category of finite probability schemes to give functorial conditional expectation, conditional independence via fiber products, Markov chains from pairwise schemes, and identifications with relative traces and Frobenius reciprocity.