About this ebook
This book reveals how univalent functions appear in quantum probability theory. Building upon the recently established one-to-one correspondence between Loewner theory and the theory of non-commutative additive processes, the author invites readers to explore the interplay between complex analysis, classical probability theory, and quantum probability theory. Monotone independence and its relations to classical, free, and Boolean independence underpin the development of ideas. Beginning with essential concepts from classical probability theory and complex analysis, the book goes on to define a quantum probability space and introduce five notions of independence. From this foundation, the central chapters explore convolutions and their respective central limit theorems; univalent functions; classical Loewner chains on the unit disk; slit mappings; and the relationship between free hemigroups, Loewner chains, and nonlinear resolvents. The final chapter offers an outlook on higher dimensional generalizations, including several open problems. Exercises with solutions invite readers to engage with the material throughout. Univalent Functions in Quantum Probability Theory is an essential resource at the intersection of previously distinct fields. Intended for graduate students and researchers alike, it assumes a solid foundation in real and complex analysis, with basic knowledge of classical probability theory and Hilbert spaces.
This book reveals how univalent functions appear in quantum probability theory. Building upon the recently established one-to-one correspondence between Loewner theory and the theory of non-commutative additive processes, the author invites readers to explore the interplay between complex analysi...
Discover more
About the author
Sebastian Schlessinger, University of Wuerzburg, Germany.
Sebastian Schlessinger, University of Wuerzburg, Germany.
Rate this ebook
Tell us what you think.
Reading information
Smartphones and tablets
Install the Google Play Books app for Android and iPad/iPhone. It syncs automatically with your account and allows you to read online or offline wherever you are.
Laptops and computers
You can listen to audiobooks purchased on Google Play using your computer's web browser.
eReaders and other devices
To read on e-ink devices like Kobo eReaders, you'll need to download a file and transfer it to your device. Follow the detailed Help Center instructions to transfer the files to supported eReaders.
