Develops and proves a Pontryagin-type maximum principle for control problems in free probability using controlled forward equations and free backward SDEs.
Ergodic theorems for semifinite von Neumann algebras. I
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Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
Ergodic averages of unimodular amenable group actions along mild Følner subsequences are dominated by those of a constructed integer-action Markov operator, transferring ergodic theorems from Z to the group setting.
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Pontryagin Maximum Principle in Free Probability Theory
Develops and proves a Pontryagin-type maximum principle for control problems in free probability using controlled forward equations and free backward SDEs.
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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.