Recent Developments In Infinite Dimensional Analysis And Quantum Probability

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles. In fact, in it the reader will find a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important recent developments in contemporary white noise analysis and some of its applications. For this reason, not only the latest results, but also motivations, explanations and connections with previous work have been included. The wealth of applications, from number theory to signal processing, from optimal filtering to information theory, from the statistics of stationary flows to quantum cable equations, show the power of white noise analysis as a tool. Beyond these, the authors emphasize its connections with practically all branches of contemporary probability, including stochastic geometry, the structure theory of stationary Gaussian processes, Neumann boundary value problems, and large deviations.

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. Contents:Probability Measures in Terms of Creation, Annihilation and Neutral Operators (L Accardi et al.)Generating Function Method for Orthogonal Polynomials and Jacobi–Szegö Parameters (N Asai et al.)Multiquantum Markov Semigroups, Interacting Branching Processes and Nonlinear Kinetic Equations. Finite Dimensional Case (V P Belavkin & C R Williams)A Note on Vacuum-Adapted Semimartingales and Monotone Independence (A C R Belton)Regular Quantum Stochastic Cocycles have Exponential Product Systems (B V R Bhat & J M Lindsay)Quantum Mechanics on the Circle Through Hopf q-Deformations of the Kinematical Algebra with Possible Applications to Lévy Processes (V K Dobrev et al.)On Algebraic and Quantum Random Walks (D Ellinas)Dual Representations for the Schrödinger Algebra (P Feinsilver & R Schott)A Limit Theorem for Conditionally Independent Beam Splittings (K H Fichtner et al.)On Quantum Logical Gates on a General Fock Space (W Freudenberg et al.)On an Argument of David Deutsch (R Gill)The Method of Double Product Integrals in Quantisation of Lie Bialgebras (R L Hudson)Asymptotics of Large Truncated Haar Unitary Matrices (J L Réffy)Three Ways to Representations of BA(E) (M Skeide)On Topological Entropy of Quotients and Extensions (J Zacharias)and other papers Readership: Researchers in the fields of probability, mathematical physics and functional analysis. Keywords:Quantum Probability;Infinite Dimensional Analysis;Mathematical Physics;Lévy Processes;Interacting Fock Space;Quantum Markov ProcessesKey Features:Reflects recent developments in the fieldsAll the articles are contributed by renowned researchers

This volume contains the latest results in the fields of quantum probability and infinite dimensional analysis. The contributions range from classical probability, 'pure' functional analysis and foundations of quantum mechanics to applications in mathematical physics, quantum information theory and modern mathematical finance. This diversity illustrates that research in quantum probability and infinite dimensional analysis is very active and strongly involved in modern mathematical developments and applications.

This proceedings volume gathers selected, peer-reviewed papers presented at the 41st International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics (QP41) that was virtually held at the United Arab Emirates University (UAEU) in Al Ain, Abu Dhabi, from March 28th to April 1st, 2021. The works cover recent developments in quantum probability and infinite dimensional analysis, with a special focus on applications to mathematical physics and quantum information theory. Covered topics include white noise theory, quantum field theory, quantum Markov processes, free probability, interacting Fock spaces, and more. By emphasizing the interconnection and interdependence of such research topics and their real-life applications, this reputed conference has set itself as a distinguished forum to communicate and discuss new findings in truly relevant aspects of theoretical and applied mathematics, notably in the field of mathematical physics, as well as an event of choice for the promotion of mathematical applications that address the most relevant problems found in industry. That makes this volume a suitable reading not only for researchers and graduate students with an interest in the field but for practitioners as well.

Infinite-dimensional analysis and quantum probability have undergone significant developments in the last few years and created many applications. This volume includes four expository articles on recent developments in quantum field theory, quantum stochastic differential equations, free probability and quantum white noise calculus, which are targeted also for graduate study. The fourteen research papers deal with most of the current topics, and their interconnections reflect a vivid development in interacting Fock space, infinite-dimensional groups, stochastic independence, non-commutative central limit theorems, stochastic geometry, and so on.

This volume consists of 18 research papers reflecting the impressive progress made in the field. It includes new results on quantum stochastic integration, the stochastic limit, quantum teleportation and other areas. Contents: Markov Property -- Recent Developments on the Quantum Markov Property (L Accardi & F Fidaleo); Stationary Quantum Stochastic Processes from the Cohomological Point of View (G G Amosov); The Feller Property of a Class of Quantum Markov Semigroups II (R Carbone & F Fagnola); Recognition and Teleportation (K-H Fichtner et al.); Prediction Errors and Completely Positive Maps (R Gohm); Multiplicative Properties of Double Stochastic Product Integrals (R L Hudson); Isometric Cocycles Related to Beam Splittings (V Liebscher); Multiplicativity via a Hat Trick (J M Lindsay & S J Wills); Dilation Theory and Continuous Tensor Product Systems of Hilbert Modules (M Skeide); Quasi-Free Fermion Planar Quantum Stochastic Integrals (W J Spring & I F Wilde); and other papers.