Download or read book Quantum Probability and Spectral Analysis of Graphs written by Akihito Hora and published by Springer Science & Business Media. This book was released on 2007-07-05 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.
Download or read book Spectral Analysis of Growing Graphs written by Nobuaki Obata and published by Springer. This book was released on 2017-02-17 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed as a concise introduction to the recent achievements on spectral analysis of graphs or networks from the point of view of quantum (or non-commutative) probability theory. The main topics are spectral distributions of the adjacency matrices of finite or infinite graphs and their limit distributions for growing graphs. The main vehicle is quantum probability, an algebraic extension of the traditional probability theory, which provides a new framework for the analysis of adjacency matrices revealing their non-commutative nature. For example, the method of quantum decomposition makes it possible to study spectral distributions by means of interacting Fock spaces or equivalently by orthogonal polynomials. Various concepts of independence in quantum probability and corresponding central limit theorems are used for the asymptotic study of spectral distributions for product graphs.This book is written for researchers, teachers, and students interested in graph spectra, their (asymptotic) spectral distributions, and various ideas and methods on the basis of quantum probability. It is also useful for a quick introduction to quantum probability and for an analytic basis of orthogonal polynomials.
Download or read book Spectral Analysis of Growing Graphs written by Nobuaki Obata and published by . This book was released on 2017 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Quantum Graphs written by Gregory Berkolaiko and published by American Mathematical Soc.. This book was released on 2013 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.
Download or read book Selected Papers on Analysis and Related Topics written by and published by American Mathematical Soc.. This book was released on 2008 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains translations of papers that originally appeared in the Japanese journal 'Sugaku'. The papers range over a variety of topics, including operator algebras, analysis, and statistics.
Download or read book Groups and Graphs Designs and Dynamics written by R. A. Bailey and published by Cambridge University Press. This book was released on 2024-05-30 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.
Download or read book Infinite Dimensional Analysis Quantum Probability And Related Topics Qp38 Proceedings Of The International Conference written by Noboru Watanabe and published by World Scientific. This book was released on 2023-10-25 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume aims to return to the starting point of the fields of infinite dimensional analysis and quantum probability, fields that are growing rapidly at present, and to seriously attempt mutual interaction between the two, with a view to enumerating and solving the many fundamental problems they entail. For such a purpose, we look for interdisciplinary bridges in mathematics including classical probability and to different branches of physics, in particular, research for new paradigms for information science on the basis of quantum theory.
Download or read book Spectral Graph Theory written by Fan R. K. Chung and published by American Mathematical Soc.. This book was released on 1997 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text discusses spectral graph theory.
Download or read book Quantum Probability written by Marek Bożejko and published by . This book was released on 2006 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Frontiers in Analysis and Probability written by Nalini Anantharaman and published by Springer Nature. This book was released on 2020-11-21 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume presents extensive research devoted to a broad spectrum of mathematical analysis and probability theory. Subjects discussed in this Work are those treated in the so-called Strasbourg–Zürich Meetings. These meetings occur twice yearly in each of the cities, Strasbourg and Zürich, venues of vibrant mathematical communication and worldwide gatherings. The topical scope of the book includes the study of monochromatic random waves defined for general Riemannian manifolds, notions of entropy related to a compact manifold of negative curvature, interacting electrons in a random background, lp-cohomology (in degree one) of a graph and its connections with other topics, limit operators for circular ensembles, polyharmonic functions for finite graphs and Markov chains, the ETH-Approach to Quantum Mechanics, 2-dimensional quantum Yang–Mills theory, Gibbs measures of nonlinear Schrödinger equations, interfaces in spectral asymptotics and nodal sets. Contributions in this Work are composed by experts from the international community, who have presented the state-of-the-art research in the corresponding problems treated. This volume is expected to be a valuable resource to both graduate students and research mathematicians working in analysis, probability as well as their interconnections and applications.
Download or read book Linear Systems Signal Processing and Hypercomplex Analysis written by Daniel Alpay and published by Springer. This book was released on 2019-08-08 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes contributions originating from a conference held at Chapman University during November 14-19, 2017. It presents original research by experts in signal processing, linear systems, operator theory, complex and hypercomplex analysis and related topics.
Download or read book Matrix Inequalities for Iterative Systems written by Hanjo Taubig and published by CRC Press. This book was released on 2017-02-03 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.
Download or read book Contributions of Mexican Mathematicians Abroad in Pure and Applied Mathematics written by Juan Carlos Pardo Millán and published by American Mathematical Soc.. This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Second Workshop of Mexican Mathematicians Abroad (II Reunión de Matemáticos Mexicanos en el Mundo), held from December 15–19, 2014, at Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. This meeting was the second in a series of ongoing biannual meetings aimed at showcasing the research of Mexican mathematicians based outside of Mexico. The book features articles drawn from eight broad research areas: algebra, analysis, applied mathematics, combinatorics, dynamical systems, geometry, probability theory, and topology. Their topics range from novel applications of non-commutative probability to graph theory, to interactions between dynamical systems and geophysical flows. Several articles survey the fields and problems on which the authors work, highlighting research lines currently underrepresented in Mexico. The research-oriented articles provide either alternative approaches to well-known problems or new advances in active research fields. The wide selection of topics makes the book accessible to advanced graduate students and researchers in mathematics from different fields.
Download or read book Proceedings of the Fourth German Japanese Symposium Infinite Dimensional Harmonic Analysis IV written by Joachim Hilgert and published by World Scientific. This book was released on 2009 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fourth Conference on Infinite Dimensional Harmonic Analysis brought together experts in harmonic analysis, operator algebras and probability theory. Most of the articles deal with the limit behavior of systems with many degrees of freedom in the presence of symmetry constraints. This volume gives new directions in research bringing together probability theory and representation theory.
Download or read book Infinite Dimensional Harmonic Analysis IV written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Progress in Nanophotonics 5 written by Takashi Yatsui and published by Springer. This book was released on 2018-08-29 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents important topics in nanophotonics in review-style chapters written by world leading scientists. The book sketches the history of dressed photon science and technology and explains why advanced theories of dressed photons are required. To meet this requirement, the recent results of theoretical studies and the theory of dressed photons are displayed by modifying the conventional electromagnetic theory. The classical theoretical model of spatiotemporal vortex dynamics is explained by treating the dressed photon as a space-like virtual photon. Also discussed in the book is the energy transfer of dressed photons, based on a quantum walk model and a quantum mechanical measurement process of dressed photons for connecting the nano- and macro-systems. Dressed photons are explained as quantum fields by characterizing them in momentum space.
Download or read book Non commutativity Infinite dimensionality and Probability at the Crossroads written by Nobuaki Obata and published by World Scientific. This book was released on 2003-01-16 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
