Download or read book Probabilistic Symmetries and Invariance Principles written by Olav Kallenberg and published by Springer Science & Business Media. This book was released on 2005-12-15 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is the first comprehensive treatment of the three basic symmetries of probability theory - contractability, exchangeability, and rotatability - defined as invariance in distribution under contractions, permutations, and rotations. Most chapters require only some basic, graduate level probability theory, and should be accessible to any serious researchers and graduate students in probability and statistics. Parts of the book may also be of interest to pure and applied mathematicians in other areas. The exposition is formally self-contained, with detailed references provided for any deeper facts from real analysis or probability used in the book."--Jacket.
Download or read book Probabilistic Symmetries and Invariance Principles written by Olav Kallenberg and published by Springer Science & Business Media. This book was released on 2005-07-27 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive treatment of the three basic symmetries of probability theory—contractability, exchangeability, and rotatability—defined as invariance in distribution under contractions, permutations, and rotations. Originating with the pioneering work of de Finetti from the 1930's, the theory has evolved into a unique body of deep, beautiful, and often surprising results, comprising the basic representations and invariance properties in one and several dimensions, and exhibiting some unexpected links between the various symmetries as well as to many other areas of modern probability. Most chapters require only some basic, graduate level probability theory, and should be accessible to any serious researchers and graduate students in probability and statistics. Parts of the book may also be of interest to pure and applied mathematicians in other areas. The exposition is formally self-contained, with detailed references provided for any deeper facts from real analysis or probability used in the book. Olav Kallenberg received his Ph.D. in 1972 from Chalmers University in Gothenburg, Sweden. After teaching for many years at Swedish universities, he moved in 1985 to the US, where he is currently Professor of Mathematics at Auburn University. He is well known for his previous books Random Measures (4th edition, 1986) and Foundations of Modern Probability (2nd edition, 2002) and for numerous research papers in all areas of probability. In 1977, he was the second recipient ever of the prestigious Rollo Davidson Prize from Cambridge University. In 1991–94, he served as the Editor in Chief of Probability Theory and Related Fields. Professor Kallenberg is an elected fellow of the Institute of Mathematical Statistics.
Download or read book Random Measures Theory and Applications written by Olav Kallenberg and published by Springer. This book was released on 2017-04-12 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.
Download or read book Foundations of Modern Probability written by Olav Kallenberg and published by Springer Nature. This book was released on 2021-02-07 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.
Download or read book Probabilistic Foundations of Statistical Network Analysis written by Harry Crane and published by CRC Press. This book was released on 2018-04-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic Foundations of Statistical Network Analysis presents a fresh and insightful perspective on the fundamental tenets and major challenges of modern network analysis. Its lucid exposition provides necessary background for understanding the essential ideas behind exchangeable and dynamic network models, network sampling, and network statistics such as sparsity and power law, all of which play a central role in contemporary data science and machine learning applications. The book rewards readers with a clear and intuitive understanding of the subtle interplay between basic principles of statistical inference, empirical properties of network data, and technical concepts from probability theory. Its mathematically rigorous, yet non-technical, exposition makes the book accessible to professional data scientists, statisticians, and computer scientists as well as practitioners and researchers in substantive fields. Newcomers and non-quantitative researchers will find its conceptual approach invaluable for developing intuition about technical ideas from statistics and probability, while experts and graduate students will find the book a handy reference for a wide range of new topics, including edge exchangeability, relative exchangeability, graphon and graphex models, and graph-valued Levy process and rewiring models for dynamic networks. The author’s incisive commentary supplements these core concepts, challenging the reader to push beyond the current limitations of this emerging discipline. With an approachable exposition and more than 50 open research problems and exercises with solutions, this book is ideal for advanced undergraduate and graduate students interested in modern network analysis, data science, machine learning, and statistics. Harry Crane is Associate Professor and Co-Director of the Graduate Program in Statistics and Biostatistics and an Associate Member of the Graduate Faculty in Philosophy at Rutgers University. Professor Crane’s research interests cover a range of mathematical and applied topics in network science, probability theory, statistical inference, and mathematical logic. In addition to his technical work on edge and relational exchangeability, relative exchangeability, and graph-valued Markov processes, Prof. Crane’s methods have been applied to domain-specific cybersecurity and counterterrorism problems at the Foreign Policy Research Institute and RAND’s Project AIR FORCE.
Download or read book Symmetry Principles Particle Physics written by W. M. Gibson and published by Cambridge University Press. This book was released on 1976-03-11 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: An understanding of the properties and interactions of the elementary particles is an essential prerequisite of research work in high energy physics. Much progress in the subject has been achieved with the aid of symmetry principles. In this 1980 book the concept of symmetry or invariance is employed as a unifying theme. Using a careful explanation of the mathematical formalism and with many applications to particular cases, the authors introduce the reader to the symmetry schemes which dominate the world of the particle physicist. The presentation will also appeal to mathematicians and physicists in other fields who are interested in the applications of the general principles of symmetry. After a brief survey of the particles and a review of the relevant quantum mechanics, the principal symmetries are studied in turn. Some technical points are relegated to appendices and the book contains extensive references.
Download or read book Origin Of Symmetries written by C D Froggatt and published by World Scientific. This book was released on 1991-08-13 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development in our understanding of symmetry principles is reviewed. Many symmetries, such as charge conjugation, parity and strangeness, are no longer considered as fundamental but as natural consequences of a gauge field theory of strong and electromagnetic interactions. Other symmetries arise naturally from physical models in some limiting situation, such as for low energy or low mass. Random dynamics and attempts to explain all symmetries — even Lorentz invariance and gauge invariance — without appealing to any fundamental invariance of the laws of nature are discussed. A selection of original papers is reprinted.
Download or read book Foundations of Modern Probability written by Olav Kallenberg and published by Springer Science & Business Media. This book was released on 2002-01-08 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.
Download or read book Computational Applications of Invariance Principles written by Raghu Vardhan Reddy Meka and published by . This book was released on 2011 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis focuses on applications of classical tools from probability theory and convex analysis such as limit theorems to problems in theoretical computer science, specifically to pseudorandomness and learning theory. At first look, limit theorems, pseudorandomness and learning theory appear to be disparate subjects. However, as it has now become apparent, there's a strong connection between these questions through a third more abstract question: what do random objects look like. This connection is best illustrated by the study of the spectrum of Boolean functions which directly or indirectly played an important role in a plethora of results in complexity theory. The current thesis aims to take this program further by drawing on a variety of fundamental tools, both classical and new, in probability theory and analytic geometry. Our research contributions broadly fall into three categories. Probability Theory: The central limit theorem is one of the most important results in all of probability and richly studied topic. Motivated by questions in pseudorandomness and learning theory we obtain two new limit theorems or invariance principles. The proofs of these new results in probability, of interest on their own, have a computer science flavor and fall under the niche category of techniques from theoretical computer science with applications in pure mathematics. Pseudorandomness: Derandomizing natural complexity classes is a fundamental problem in complexity theory, with several applications outside complexity theory. Our work addresses such derandomization questions for natural and basic geometric concept classes such as halfspaces, polynomial threshold functions (PTFs) and polytopes. We develop a reasonably generic framework for obtaining pseudorandom generators (PRGs) from invariance principles and suitably apply the framework to old and new invariance principles to obtain the best known PRGs for these complexity classes. Learning Theory: Learning theory aims to understand what functions can be learned efficiently from examples. As developed in the seminal work of Linial, Mansour and Nisan (1994) and strengthened by several follow-up works, we now know strong connections between learning a class of functions and how sensitive to noise, as quantified by average sensitivity and noise sensitivity, the functions are. Besides their applications in learning, bounding the average and noise sensitivity has applications in hardness of approximation, voting theory, quantum computing and more. Here we address the question of bounding the sensitivity of polynomial threshold functions and intersections of halfspaces and obtain the best known results for these concept classes.
Download or read book Journal of the American Statistical Association written by and published by . This book was released on 2008 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Invariance Principles for Self randomized Student Processes written by Yuliya V. Martsynyuk and published by . This book was released on 2007 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rendiconti di matematica e delle sue applicazioni written by and published by . This book was released on 2008 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Invariance Principles Return Times and Reconstruction Theorems for Random Walks in Random Environments written by John Raymond Hoffman and published by . This book was released on 1993 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Symmetry Principles in Physics written by T. D. Lee and published by . This book was released on 1970 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Symmetries in Physics written by Katherine Brading and published by Cambridge University Press. This book was released on 2003-12-04 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together philosophical discussions of symmetry in physics, highlighting the main issues and controversies. It covers all the fundamental symmetries of modern physics, as well as discussing symmetry-breaking and general interpretational issues. For each topic, classic texts are followed by review articles and short commentaries.
Download or read book Quantum Worlds written by Olimpia Lombardi and published by Cambridge University Press. This book was released on 2019-04-11 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a comprehensive and up-to-date volume on the conceptual and philosophical problems related to the interpretation of quantum mechanics.
Download or read book The British National Bibliography written by Arthur James Wells and published by . This book was released on 2007 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt:
