Given two polynomials $ p (x), q (x) $ of degree $ d $, we give a combinatorial formula for
the finite free cumulants of $ p (x)\boxtimes _d q (x) $. We show that this formula admits a …

UNIVERSITY OF CALIFORNIA Los Angeles Evolution equations in non-commutative
probability A dissertation submitted in partial sati Page 1 UNIVERSITY OF CALIFORNIA Los …

We adapt the theory of chordal Loewner chains to the operator-valued matricial upper-half
plane over a C⁎-algebra A. We define an A-valued chordal Loewner chain as a …

Cyclic monotone independence is an algebraic notion of noncommutative independence,
introduced in the study of multi-matrix random matrix models with small rank. Its algebraic …

In\cite {EjsmontLehner: 2020: tangent} we study the limit sums of free commutators and
anticommutators and show that the generalized tangent function $$\frac {\tan z}{1-x\tan z} …

The main purpose of this paper is to study time-inhomogeneous one-dimensional branching
processes (mainly on a continuous but also on a discrete state space) with the help of recent …

We consider multiple radial SLE as the number of curves tends to infinity. We give conditions
that imply the tightness of the associated processes given by the Loewner equation. In the …

One-parameter semigroups of holomorphic functions appear naturally in various
applications of Complex Analysis, and in particular, in the theory of (temporally) …

This paper introduces the class of selfdecomposable distributions concerning Boolean
convolution. A general regularity property of Boolean selfdecomposable distributions is …

In this article, we prove that nonlinear resolvents of infinitesimal generators on bounded and
convex subdomains of C n are decreasing Loewner chains. Furthermore, we consider the …