The Chordal Loewner Equation and Monotone Probability Theory
Sebastian Schlei{\ss}inger
TL;DR
This paper explores the chordal Loewner equation through the lens of non-commutative probability, connecting it with monotone, anti-monotone, and free probability theories to understand their evolution equations.
Contribution
It identifies the chordal Loewner equations as non-autonomous evolution equations within various non-commutative probability frameworks, extending prior interpretations.
Findings
Links chordal Loewner equations to monotone and anti-monotone probability theory
Establishes the equations as non-autonomous evolution equations
Provides insights into free probability theory connections
Abstract
In [5], O. Bauer interpreted the chordal Loewner equation in terms of non-commutative probability theory. We follow this perspective and identify the chordal Loewner equations as the non-autonomous versions of evolution equations for semigroups in monotone and anti-monotone probability theory. We also look at the corresponding equation for free probability theory.
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