Probability And Randomness
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Probability And Randomness
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Author : Andre? I?U?r?evich Khrennikov
language : en
Publisher: World Scientific
Release Date : 2016
Probability And Randomness written by Andre? I?U?r?evich Khrennikov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Science categories.
"Creating a rigorous mathematical theory of randomness is far from being complete, even in the classical case. Interrelation of Classical and Quantum Randomness rectifies this and introduces mathematical formalisms of classical and quantum probability and randomness with brief discussion of their interrelation and interpretational and foundational issues. The book presents the essentials of classical approaches to randomness, enlightens their successes and problems, and then proceeds to essentials of quantum randomness. Its wide-ranging and comprehensive scope makes it suitable for researchers in mathematical physics, probability and statistics at any level"--
Probability And Random Number A First Guide To Randomness
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Author : Sugita Hiroshi
language : en
Publisher: World Scientific
Release Date : 2017-10-06
Probability And Random Number A First Guide To Randomness written by Sugita Hiroshi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-06 with Mathematics categories.
This is a book of elementary probability theory that includes a chapter on algorithmic randomness. It rigorously presents definitions and theorems in computation theory, and explains the meanings of the theorems by comparing them with mechanisms of the computer, which is very effective in the current computer age. Random number topics have not been treated by any books on probability theory, only some books on computation theory. However, the notion of random number is necessary for understanding the essential relation between probability and randomness. The field of probability has changed very much, thus this book will make and leave a big impact even to expert probabilists. Readers from applied sciences will benefit from this book because it presents a very proper foundation of the Monte Carlo method with practical solutions, keeping the technical level no higher than 1st year university calculus. Contents: Mathematics of Coin TossingMathematical ModelRandom NumberLimit TheoremMonte Carlo MethodInfinite coin TossesRandom Number: Recursive FunctionKolmogorov Complexity and Random NumberLimit Theorem: Bernoulli's TheoremLaw of Large NumbersDe Moivre–Laplace's TheoremCentral Limit TheoremMathematical StatisticsMonte Carlo Method: Monte Carlo Method as GamblingPseudorandom GeneratorMonte Carlo IntegrationFrom the Viewpoint of Mathematical StatisticsAppendices: Symbols and TermsBinary Numeral SystemLimit of Sequence and FunctionLimits of Exponential Function and LogarithmC Language Program Readership: First year university students to professionals. Keywords: Probability;Probability Theory;Randomness;Random Number;Pseudorandom Number;Monte Carlo Method;Monte Carlo IntegrationReview: Key Features: This is the first book that presents both probability theory and algorithmic randomness for from 1st year university students to experts. It is technically easy but worth reading for experts as wellThis book presents basic limit theorems with proofs that are not seen in usual probability textbooks; for readers should learn that a good solution is not always uniqueThis book rigorously treats the Monte Carlo method. In particular, it presents the random Weyl sampling, which produces pseudorandom numbers for the Monte Carlo integration that act complete substitutes for random numbers
Probability And Randomness
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Author : Andrei Khrennikov
language : en
Publisher: World Scientific
Release Date : 2016-03-04
Probability And Randomness written by Andrei Khrennikov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-04 with Mathematics categories.
' Creating a rigorous mathematical theory of randomness is far from being complete, even in the classical case. Probability and Randomness: Quantum versus Classical rectifies this and introduces mathematical formalisms of classical and quantum probability and randomness with brief discussion of their interrelation and interpretational and foundational issues. The book presents the essentials of classical approaches to randomness, enlightens their successes and problems, and then proceeds to essentials of quantum randomness. Its wide-ranging and comprehensive scope makes it suitable for researchers in mathematical physics, probability and statistics at any level. Contents:Foundations of ProbabilityRandomnessSupplementary Notes on Measure-theoretic and Frequency ApproachesIntroduction to Quantum FormalismQuantum and Contextual ProbabilityInterpretations of Quantum Mechanics and ProbabilityRandomness: Quantum Versus ClassicalProbabilistic Structure of Bell''s ArgumentQuantum Probability Outside of Physics: from Molecular Biology to Cognition Readership: Researchers in mathematical physics, probability and statistics. Keywords:Kolmogorov Axiomataics;Randomness;Independence;Quantum Probability'
Probability And Random Processes
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Author : Geoffrey Grimmett
language : en
Publisher: Oxford University Press
Release Date : 2001-05-31
Probability And Random Processes written by Geoffrey Grimmett and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-31 with Mathematics categories.
This textbook provides a wide-ranging and entertaining indroduction to probability and random processes and many of their practical applications. It includes many exercises and problems with solutions.
Randomness
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Author : Deborah J. Bennett
language : en
Publisher: Harvard University Press
Release Date : 2009-07-01
Randomness written by Deborah J. Bennett and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-01 with Philosophy categories.
From the ancients' first readings of the innards of birds to your neighbor's last bout with the state lottery, humankind has put itself into the hands of chance. Today life itself may be at stake when probability comes into play--in the chance of a false negative in a medical test, in the reliability of DNA findings as legal evidence, or in the likelihood of passing on a deadly congenital disease--yet as few people as ever understand the odds. This book is aimed at the trouble with trying to learn about probability. A story of the misconceptions and difficulties civilization overcame in progressing toward probabilistic thinking, Randomness is also a skillful account of what makes the science of probability so daunting in our own day. To acquire a (correct) intuition of chance is not easy to begin with, and moving from an intuitive sense to a formal notion of probability presents further problems. Author Deborah Bennett traces the path this process takes in an individual trying to come to grips with concepts of uncertainty and fairness, and also charts the parallel path by which societies have developed ideas about chance. Why, from ancient to modern times, have people resorted to chance in making decisions? Is a decision made by random choice fair? What role has gambling played in our understanding of chance? Why do some individuals and societies refuse to accept randomness at all? If understanding randomness is so important to probabilistic thinking, why do the experts disagree about what it really is? And why are our intuitions about chance almost always dead wrong? Anyone who has puzzled over a probability conundrum is struck by the paradoxes and counterintuitive results that occur at a relatively simple level. Why this should be, and how it has been the case through the ages, for bumblers and brilliant mathematicians alike, is the entertaining and enlightening lesson of Randomness.
Quantum Probability And Randomness
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Author : Andrei Khrennikov
language : en
Publisher: MDPI
Release Date : 2019-04-18
Quantum Probability And Randomness written by Andrei Khrennikov and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-18 with Science categories.
The last few years have been characterized by a tremendous development of quantum information and probability and their applications, including quantum computing, quantum cryptography, and quantum random generators. In spite of the successful development of quantum technology, its foundational basis is still not concrete and contains a few sandy and shaky slices. Quantum random generators are one of the most promising outputs of the recent quantum information revolution. Therefore, it is very important to reconsider the foundational basis of this project, starting with the notion of irreducible quantum randomness. Quantum probabilities present a powerful tool to model uncertainty. Interpretations of quantum probability and foundational meaning of its basic tools, starting with the Born rule, are among the topics which will be covered by this issue. Recently, quantum probability has started to play an important role in a few areas of research outside quantum physics—in particular, quantum probabilistic treatment of problems of theory of decision making under uncertainty. Such studies are also among the topics of this issue.
What Is Random
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Author : Edward Beltrami
language : en
Publisher: Springer Nature
Release Date : 2020-07-30
What Is Random written by Edward Beltrami and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-30 with Mathematics categories.
In this fascinating book, mathematician Ed Beltrami takes a close enough look at randomness to make it mysteriously disappear. The results of coin tosses, it turns out, are determined from the start, and only our incomplete knowledge makes them look random. "Random" sequences of numbers are more elusive, but Godels undecidability theorem informs us that we will never know. Those familiar with quantum indeterminacy assert that order is an illusion, and that the world is fundamentally random. Yet randomness is also an illusion. Perhaps order and randomness, like waves and particles, are only two sides of the same (tossed) coin.
Introduction To Random Time And Quantum Randomness
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Author : Kai Lai Chung
language : en
Publisher: World Scientific
Release Date : 2003
Introduction To Random Time And Quantum Randomness written by Kai Lai Chung and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Science categories.
This book is made up of two essays on the role of time in probability and quantum physics. In the first one, K L Chung explains why, in his view, probability theory starts where random time appears. This idea is illustrated in various probability schemes and the deep impact of those random times on the theory of the stochastic process is shown. In the second essay J-C Zambrini shows why quantum physics is not a regular probabilistic theory, but also why stochastic analysis provides new tools for analyzing further the meaning of Feynman's path integral approach and a number of foundational issues of quantum physics far beyond what is generally considered. The role of the time parameter, in this theory, is critically re-examined and a fresh way to approach the long-standing problem of the quantum time observable is suggested.
Struck By Lightning
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Author : Jeffrey S. Rosenthal
language : en
Publisher: Granta Books
Release Date : 2014-03-06
Struck By Lightning written by Jeffrey S. Rosenthal and has been published by Granta Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-06 with Mathematics categories.
Human beings have long been both fascinated and appalled by randomness. On the one hand, we love the thrill of a surprise party or the freedom of not knowing what tomorrow will bring. We are inexplicably delighted by strange coincidences and striking similarities. But we also hate uncertainty's dark side. From cancer to bird flu, diseases may strike with no apparent pattern. Terrorists attack, airplanes crash, bridges collapse, and we never know if we'll be that one-in-a-million statistic. In this entertaining look at the world of probabilities, Jeffrey Rosenthal, maths professor and improvisational comedian, explains the mechanics of randomness in fields as diverse as poker hands, email spam, crime statistics, opinion polls and lottery jackpots. Read Struck by Lightning and, chances are, you will never look at the world the same way again.
Understanding Probability
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Author : Henk Tijms
language : en
Publisher: Cambridge University Press
Release Date : 2012-06-14
Understanding Probability written by Henk Tijms 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 2012-06-14 with Mathematics categories.
Using everyday examples to demystify probability, this classic is now in its third edition with new chapters, exercises and examples.