The chordal Loewner equation and monotone probability theory

In Ref. 5, O. Bauer interpreted the chordal Loewner equation in terms of noncommutative 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.