Univalent functions in quantum probability theory /
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,...
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| Format: | Book |
| Language: | English |
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Providence, Rhode Island :
American Mathematical Society,
[2025].
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| Series: | Mathematical surveys and monographs ;
no. 294. |
| Subjects: |
| Summary: | 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. |
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| Physical Description: | x, 268 pages : chiefly color illustrations ; 26 cm. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781470481803 1470481804 |