White Noise On Bialgebras
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| Author | : Michael Schürmann |
| Publisher | : Springer |
| Total Pages | : 152 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540476148 |
Stochastic processes with independent increments on a group are generalized to the concept of "white noise" on a Hopf algebra or bialgebra. The main purpose of the book is the characterization of these processes as solutions of quantum stochastic differential equations in the sense of R.L. Hudsonand K.R. Parthasarathy. The notes are a contribution to quantum probability but they are also related to classical probability, quantum groups, and operator algebras. The Az ma martingales appear as examples of white noise on a Hopf algebra which is a deformation of the Heisenberg group. The book will be of interest to probabilists and quantum probabilists. Specialists in algebraic structures who are curious about the role of their concepts in probablility theory as well as quantum theory may find the book interesting. The reader should havesome knowledge of functional analysis, operator algebras, and probability theory.
| Author | : U. Franz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 233 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 9401592772 |
This book aims to present several new developments on stochastic processes and operator calculus on quantum groups. Topics which are treated include operator calculus, dual representations, stochastic processes and diffusions, Appell polynomials and systems in connection with evolution equations. Audience: This volume contains introductory material for graduate students who are new to the field, as well as more advanced material for specialists in probability theory, algebraic structures, representation theory, mathematical physics and theoretical physics.
| Author | : V. P. Belavkin |
| Publisher | : World Scientific |
| Total Pages | : 410 |
| Release | : 2008 |
| Genre | : Science |
| ISBN | : 9812832963 |
Quantum stochastic calculus has become an indispensable tool in modern quantum physics, its effectiveness being illustrated by recent developments in quantum control which place the calculus at the heart of the theory. Quantum statistics is rapidly taking shape as an intrinsically quantum counterpart to classical statistics, motivated by advances in quantum engineering and the need for better statistical inference tools for quantum systems.This volume contains a selection of regular research articles and reviews by leading researchers in quantum control, quantum statistics, quantum probability and quantum information. The selection offers a unified view of recent trends in quantum stochastics, highlighting the common mathematical language of Hilbert space operators, and the deep connections between classical and quantum stochastic phenomena.
| Author | : I. Cuculescu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 367 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 9401583749 |
The intention of this book is to explain to a mathematician having no previous knowledge in this domain, what "noncommutative probability" is. So the first decision was not to concentrate on a special topic. For different people, the starting points of such a domain may be different. In what concerns this question, different variants are not discussed. One such variant comes from Quantum Physics. The motivations in this book are mainly mathematical; more precisely, they correspond to the desire of developing a probability theory in a new set-up and obtaining results analogous to the classical ones for the newly defined mathematical objects. Also different mathematical foundations of this domain were proposed. This book concentrates on one variant, which may be described as "von Neumann algebras". This is true also for the last chapter, if one looks at its ultimate aim. In the references there are some papers corresponding to other variants; we mention Gudder, S.P. &al (1978). Segal, I.E. (1965) also discusses "basic ideas".
| Author | : Rolando Rebolledo |
| Publisher | : World Scientific |
| Total Pages | : 339 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 9814338737 |
This volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.
| Author | : Rolando Rebolledo |
| Publisher | : World Scientific |
| Total Pages | : 339 |
| Release | : 2011-01-19 |
| Genre | : Mathematics |
| ISBN | : 9814462179 |
This volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.
| Author | : R. L. Hudson |
| Publisher | : World Scientific |
| Total Pages | : 376 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 9789810235413 |
Much has changed in the world of quantum probability since the publication of the last volume in this series. Giants in the field, such as P-A Meyer, K R Parthasarathy and W von Waldenfels, have reached the age of retirement. Readers will, however, be pleased to see evidence in the present volume that Partha remains as creatively active as ever. The field itself, regarded at one time as the esoteric province of a small group of devotees, has come of age. It has attracted the enthusiastic commitment of an ever-growing army of young mathematicians and physicists, many of whom are represented here.
| Author | : Roland Speicher |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 105 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0821806939 |
Free probability theory, introduced by Voiculescu, has developed very actively in the last few years and has had an increasing impact on quite different fields in mathematics and physics. Whereas the subject arose out of the field of von Neumann algebras, presented here is a quite different view of Voiculescu's amalgamated free product. This combinatorial description not only allows re-proving of most of Voiculescu's results in a concise and elegant way, but also opens the way for many new results. Unlike other approaches, this book emphasizes the combinatorial structure of the concept of ``freeness''. This gives an elegant and easily accessible description of freeness and leads to new results in unexpected directions. Specifically, a mathematical framework for otherwise quite ad hoc approximations in physics emerges.
| Author | : Uwe Franz |
| Publisher | : Cambridge University Press |
| Total Pages | : 200 |
| Release | : 2016-01-07 |
| Genre | : Mathematics |
| ISBN | : 1316674045 |
Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known 'commutative' results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physics and operator algebras.
| Author | : Uwe Franz |
| Publisher | : World Scientific |
| Total Pages | : 547 |
| Release | : 2005-01-12 |
| Genre | : Mathematics |
| ISBN | : 9814481025 |
This volume collects research papers in quantum probability and related fields and reflects the recent developments in quantum probability ranging from the foundations to its applications.
