David Jekel's Research

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Notes on Operator-valued Noncommutative Probability

Operator-Valued Noncommutative Probability. (169 pages)
These notes are a systematic exposition / reference for results on free, boolean, and monotone independence, and they include a few new results as well. They are a work in progress, and several more chapters are planned. I welcome editorial feedback. Last updated November 19, 2018.

Papers and Preprints

  1. An Elementary Approach to Free Entropy Theory for Convex Potentials.
    Preprint May 2018
    arXiv 1805.08814
    Talk Slides--shorter, less technical
    Talk Slides--longer, more technical
  2. Operator-valued Chordal Loewner Chains and Non-Commutative Probability.
    Preprint November 2017
    arXiv 1711.02611
    Talk Slides
  3. Algebraic Properties of Generalized Graph Laplacians: Resistor Networks, Critical Groups, and Homological Algebra.
    (With Avi Levy, Will Dana, Austin Stromme, Collin Litterell)
    SIAM J. Discrete Math 32-2 (2018), pp. 1040-1110.
    Final Version PDF
    arXiv 1604.07075

Miscellaneous Notes