Special Issue on Non-Commutative Algebra, Probability and Analysis in Action

The Guest Editors for this special issue are

Joscha Diehl (University of Greifswald, Germany)
Kurusch Ebrahimi-Fard (Norwegian University of Science and Technology Trondheim, Norway)
Uwe Franz (University of Bourgogne Franche-Comté, France)
Malte Gerhold (University of Greifswald, Germany)
Nikolas Tapia (Weierstraß Institute for Applied Analysis and Stochastics & TU Berlin, Germany)

This special issue is dedicated to the intriguing ramifications of non-commutative algebra in probability, analysis and data science, as reflected in the following topics:

• non-commutative probability theory,
• stochastic processes on quantum groups,
• signature methods in data science,
• random matrices and their applications,
• Hopf algebras in combinatorics and stochastic.

It is related to the conference held in honour of Michael Schürmann on the occasion of the retirement from his professorship at the Department of Mathematics and Computer Science of the University of Greifswald, Germany. The conference took place at the Alfried Krupp Wissenschaftskolleg in Greifswald, from 20–25 September, 2021.

The volume consists of 14 papers for a total of 323 pages.

We are grateful to all the authors who contributed to this volume and to the referees for providing constructive reviews.

Papers in this Issue:

The Double Fock Space of Type B

Marek Bożejko and Wiktor Ejsmont
SIGMA 19 (2023), 040, 22 pages   [ abs   pdf ]

Shifted Substitution in Non-Commutative Multivariate Power Series with a View Toward Free Probability

Kurusch Ebrahimi-Fard, Frédéric Patras, Nikolas Tapia and Lorenzo Zambotti
SIGMA 19 (2023), 038, 17 pages   [ abs   pdf ]

Shuffle Algebras and Non-Commutative Probability for Pairs of Faces

Joscha Diehl, Malte Gerhold and Nicolas Gilliers
SIGMA 19 (2023), 006, 50 pages   [ abs   pdf ]

On the Signature of a Path in an Operator Algebra

Nicolas Gilliers and Carlo Bellingeri
SIGMA 18 (2022), 096, 43 pages   [ abs   pdf ]

Markovianity and the Thompson Group $F$

Claus Köstler and Arundhathi Krishnan
SIGMA 18 (2022), 083, 27 pages   [ abs   pdf ]

Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections

W. Steven Gray
SIGMA 18 (2022), 082, 15 pages   [ abs   pdf ]

Categorial Independence and Lévy Processes

Malte Gerhold, Stephanie Lachs and Michael Schürmann
SIGMA 18 (2022), 075, 27 pages   [ abs   pdf ]

Monotone Cumulant-Moment Formula and Schröder Trees

Octavio Arizmendi and Adrian Celestino
SIGMA 18 (2022), 073, 22 pages   [ abs   pdf ]

Spatial Markov Semigroups Admit Hudson-Parthasarathy Dilations

Michael Skeide
SIGMA 18 (2022), 071,   8 pages   [ abs   pdf ]

De Finetti Theorems for the Unitary Dual Group

Isabelle Baraquin, Guillaume Cébron, Uwe Franz, Laura Maassen and Moritz Weber
SIGMA 18 (2022), 067, 29 pages   [ abs   pdf ]

Maximal Discrete Subgroups in Unitary Groups of Operator Algebras

Vadim Alekseev and Andreas Thom
SIGMA 18 (2022), 052,   7 pages   [ abs   pdf ]

Functional Equations Solving Initial-Value Problems of Complex Burgers-Type Equations for One-Dimensional Log-Gases

Taiki Endo, Makoto Katori and Noriyoshi Sakuma
SIGMA 18 (2022), 049, 22 pages   [ abs   pdf ]

Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams

John E. Gough
SIGMA 18 (2022), 044, 15 pages   [ abs   pdf ]

The Generalized Fibonacci Oscillator as an Open Quantum System

Franco Fagnola, Chul Ki Ko and Hyun Jae Yoo
SIGMA 18 (2022), 035, 19 pages   [ abs   pdf ]