Probabilistic Techniques In Analysis
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Probabilistic Techniques In Analysis
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Author : Richard F. Bass
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-12-16
Probabilistic Techniques In Analysis written by Richard F. Bass and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-16 with Mathematics categories.
In recent years, there has been an upsurge of interest in using techniques drawn from probability to tackle problems in analysis. These applications arise in subjects such as potential theory, harmonic analysis, singular integrals, and the study of analytic functions. This book presents a modern survey of these methods at the level of a beginning Ph.D. student. Highlights of this book include the construction of the Martin boundary, probabilistic proofs of the boundary Harnack principle, Dahlberg's theorem, a probabilistic proof of Riesz' theorem on the Hilbert transform, and Makarov's theorems on the support of harmonic measure. The author assumes that a reader has some background in basic real analysis, but the book includes proofs of all the results from probability theory and advanced analysis required. Each chapter concludes with exercises ranging from the routine to the difficult. In addition, there are included discussions of open problems and further avenues of research.
Probability And Computing
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Author : Michael Mitzenmacher
language : en
Publisher: Cambridge University Press
Release Date : 2005-01-31
Probability And Computing written by Michael Mitzenmacher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-31 with Computers categories.
Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.
The Probabilistic Method
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Author : Noga Alon
language : en
Publisher: John Wiley & Sons
Release Date : 2015-11-02
The Probabilistic Method written by Noga Alon and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-02 with Mathematics categories.
Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.
Probabilistic Methods In Geotechnical Engineering
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Author : D. V. Griffiths
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-14
Probabilistic Methods In Geotechnical Engineering written by D. V. Griffiths and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-14 with Science categories.
Learn to use probabilistic techniques to solve problems in geotechnical engineering. The book reviews the statistical theories needed to develop the methodologies and interpret the results. Next, the authors explore probabilistic methods of analysis, such as the first order second moment method, the point estimate method, and random set theory. Examples and case histories guide you step by step in applying the techniques to particular problems.
The Probabilistic Method
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Author : Noga Alon
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-20
The Probabilistic Method written by Noga Alon and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-20 with Mathematics categories.
Praise for the Second Edition: "Serious researchers in combinatorics or algorithm design will wish to read the book in its entirety...the book may also be enjoyed on a lighter level since the different chapters are largely independent and so it is possible to pick out gems in one's own area..." —Formal Aspects of Computing This Third Edition of The Probabilistic Method reflects the most recent developments in the field while maintaining the standard of excellence that established this book as the leading reference on probabilistic methods in combinatorics. Maintaining its clear writing style, illustrative examples, and practical exercises, this new edition emphasizes methodology, enabling readers to use probabilistic techniques for solving problems in such fields as theoretical computer science, mathematics, and statistical physics. The book begins with a description of tools applied in probabilistic arguments, including basic techniques that use expectation and variance as well as the more recent applications of martingales and correlation inequalities. Next, the authors examine where probabilistic techniques have been applied successfully, exploring such topics as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Sections labeled "The Probabilistic Lens" offer additional insights into the application of the probabilistic approach, and the appendix has been updated to include methodologies for finding lower bounds for Large Deviations. The Third Edition also features: A new chapter on graph property testing, which is a current topic that incorporates combinatorial, probabilistic, and algorithmic techniques An elementary approach using probabilistic techniques to the powerful Szemerédi Regularity Lemma and its applications New sections devoted to percolation and liar games A new chapter that provides a modern treatment of the Erdös-Rényi phase transition in the Random Graph Process Written by two leading authorities in the field, The Probabilistic Method, Third Edition is an ideal reference for researchers in combinatorics and algorithm design who would like to better understand the use of probabilistic methods. The book's numerous exercises and examples also make it an excellent textbook for graduate-level courses in mathematics and computer science.
Probabilistic Risk Analysis
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Author : Tim Bedford
language : en
Publisher: Cambridge University Press
Release Date : 2001-04-30
Probabilistic Risk Analysis written by Tim Bedford and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-30 with Mathematics categories.
Probabilistic risk analysis aims to quantify the risk caused by high technology installations. Increasingly, such analyses are being applied to a wider class of systems in which problems such as lack of data, complexity of the systems, uncertainty about consequences, make a classical statistical analysis difficult or impossible. The authors discuss the fundamental notion of uncertainty, its relationship with probability, and the limits to the quantification of uncertainty. Drawing on extensive experience in the theory and applications of risk analysis, the authors focus on the conceptual and mathematical foundations underlying the quantification, interpretation and management of risk. They cover standard topics as well as important new subjects such as the use of expert judgement and uncertainty propagation. The relationship of risk analysis with decision making is highlighted in chapters on influence diagrams and decision theory. Finally, the difficulties of choosing metrics to quantify risk, and current regulatory frameworks are discussed.
Probabilistic Techniques In Exposure Assessment
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Author : Alison C. Cullen
language : en
Publisher: Springer
Release Date : 1999-07-31
Probabilistic Techniques In Exposure Assessment written by Alison C. Cullen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-31 with Medical categories.
In this text, experts provide a complete sourcebook on methods for addressing variability and uncertainty in exposure analysis.
Probabilistic Methods Applied To Electric Power Systems
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Author : Samy G. Krishnasamy
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Probabilistic Methods Applied To Electric Power Systems written by Samy G. Krishnasamy and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Technology & Engineering categories.
Probabilistic Methods Applied to Electric Power Systems contains the proceedings of the First International Symposium held in Toronto, Ontario, Canada, on July 11-13, 1986. The papers explore significant technical advances that have been made in the application of probability methods to the design of electric power systems. This volume is comprised of 65 chapters divided into 10 sections and begins by discussing the probabilistic methodologies used in the assessment of power system reliability and structural design. The following chapters focus on the applications of probabilistic techniques to the analysis and design of transmission systems and structures; evaluation of design and reliability of distribution systems; system planning; and assessment of performance of transmission system components such as insulators, tower joints, and foundations. The probability-based procedures for dealing with data bases such as wind load and ice load are also considered, along with the effects of weather-induced loads on overhead power lines and the use of probability methods in upgrading existing power lines and components. The final section deals with applications of probability methods to power system problems not covered in other chapters. This book will be of value to engineers involved in uprating, designing, analyzing, and assessing reliability of transmission and distribution systems.
Analysis In Banach Spaces
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Author : Tuomas Hytönen
language : en
Publisher: Springer
Release Date : 2018-02-14
Analysis In Banach Spaces written by Tuomas Hytönen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-14 with Mathematics categories.
This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.
Introduction To Probabilistic And Statistical Methods With Examples In R
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Author : Katarzyna Stapor
language : en
Publisher: Springer Nature
Release Date : 2020-05-22
Introduction To Probabilistic And Statistical Methods With Examples In R written by Katarzyna Stapor and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-22 with Mathematics categories.
This book strikes a healthy balance between theory and applications, ensuring that it doesn’t offer a set of tools with no mathematical roots. It is intended as a comprehensive and largely self-contained introduction to probability and statistics for university students from various faculties, with accompanying implementations of some rudimentary statistical techniques in the language R. The content is divided into three basic parts: the first includes elements of probability theory, the second introduces readers to the basics of descriptive and inferential statistics (estimation, hypothesis testing), and the third presents the elements of correlation and linear regression analysis. Thanks to examples showing how to approach real-world problems using statistics, readers will acquire stronger analytical thinking skills, which are essential for analysts and data scientists alike.