probabilistic symmetries and invariance principles probability and its applications

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Probabilistic Symmetries And Invariance Principles

Author : Olav Kallenberg
ISBN : 9780387288611
Genre : Mathematics
File Size : 66. 98 MB
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"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.

Quantum Symmetries

Author : Guillaume Aubrun
ISBN : 9783319632063
Genre : Mathematics
File Size : 68. 89 MB
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Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems. A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions. The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The latter applications will also be of interest to theoretical and mathematical physicists working in quantum theory.

Probabilistic Foundations Of Statistical Network Analysis

Author : Harry Crane
ISBN : 9781351807333
Genre : Business & Economics
File Size : 73. 44 MB
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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.

Quantum Probability And Infinite Dimensional Analysis

Author :
ISBN : 9789814465632
Genre :
File Size : 63. 19 MB
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Random Measures Theory And Applications

Author : Olav Kallenberg
ISBN : 9783319415987
Genre : Mathematics
File Size : 38. 4 MB
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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.

Journal Of The American Statistical Association

Author :
ISBN : UOM:39015072641353
Genre : Statistics
File Size : 47. 66 MB
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Symbolic And Quantitative Approaches To Reasoning With Uncertainty

Author : Thomas D. Nielsen
ISBN : 9783540404941
Genre : Computers
File Size : 62. 9 MB
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Since 1991, the European Conference on Symbolic and Quantitative Appr- ches to Reasoning with Uncertainty (ECSQARU) has been a major forum for advances in the theory and practice of reasoning and decision making under - certainty. The scope of ECSQARU is wide and includes, but is not limited to, fundamental issues, representation, inference, learning, and decision making in qualitative and numeric paradigms. The ?rst ECSQARU conference (1991) was held in Marseilles, and since then it has been held in Granada (1993), Fribourg (1995), Bonn (1997), London (1999) and Toulouse (2001). This volume contains the papers that were presented at ECSQARU 2003, held at Aalborg University, Denmark, from July 2 to July 5, 2003. The papers went through a rigorous reviewing process: three program committee members reviewed each paper monitored by an area chair, who made a ?nal recomm- dation to the program co-chairs. In addition to the regular presentations, the technical program for ECSQARU 2003 also included talks by three distingu- hedinvitedspeakers:DidierDubois,PhilippeSmetsandJeroenVermunt.Didier Dubois and Jeroen Vermunt also contributed to this volume with papers on the subjects of their talks.

Physical And Mathematical Foundations Of Probabilistic Engineering Design With Applications To Rotors

Author : John Friedrich Shortle
ISBN : UCAL:C3403678
Genre :
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High Dimensional Probability Ii

Author : Evarist Giné
ISBN : 9781461213581
Genre : Mathematics
File Size : 44. 23 MB
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High dimensional probability, in the sense that encompasses the topics rep resented in this volume, began about thirty years ago with research in two related areas: limit theorems for sums of independent Banach space valued random vectors and general Gaussian processes. An important feature in these past research studies has been the fact that they highlighted the es sential probabilistic nature of the problems considered. In part, this was because, by working on a general Banach space, one had to discard the extra, and often extraneous, structure imposed by random variables taking values in a Euclidean space, or by processes being indexed by sets in R or Rd. Doing this led to striking advances, particularly in Gaussian process theory. It also led to the creation or introduction of powerful new tools, such as randomization, decoupling, moment and exponential inequalities, chaining, isoperimetry and concentration of measure, which apply to areas well beyond those for which they were created. The general theory of em pirical processes, with its vast applications in statistics, the study of local times of Markov processes, certain problems in harmonic analysis, and the general theory of stochastic processes are just several of the broad areas in which Gaussian process techniques and techniques from probability in Banach spaces have made a substantial impact. Parallel to this work on probability in Banach spaces, classical proba bility and empirical process theory were enriched by the development of powerful results in strong approximations.

Mathematical Reviews

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ISBN : UOM:39015057109889
Genre : Mathematics
File Size : 35. 27 MB
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