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 form a category for finite probability that unifies quotients, random variable algebras, and conditionals, with linear functors constructing conditional expectation and fiber products encoding conditional independence and Markov chains.
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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
Bundles form a category for finite probability that unifies quotients, random variable algebras, and conditionals, with linear functors constructing conditional expectation and fiber products encoding conditional independence and Markov chains.