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Ergodicity (3rd edition)

Author: Luca Dellanna

Publisher: Luca Dell'anna

Published: 2020-11-08

Total Pages: 182

ISBN-13:

Some reviews of Luca's previous books "This book is like a magnificent suspension bridge, linking the science of the human brain to the practical craft of applying it in everyday life. I loved it." – Rory Sutherland, Ogilvy's Vice Chairman “So insightful with common sense applications of Complexity and the ability to communicate clearly!!” – Bob Klapetzky. “A SUPERB book [...] by one of the profound thinkers in our field [behavioral economics].” – Michal G. Bartlett What's ergodicity, and why it matters? "The Most Important Property to Understand in Probability, in Life, in Anything." – Nassim Nicholas Taleb on ergodicity. "I think the most under-rated idea is ergodicity." – David Perell, author. Is ergodicity the most important concept in decision-making and behavioral sciences? (Yes.) Is it relevant for you in your daily life? (Yes.) Is it possible to explain it so simply that a grandma or a high-schooler can understand it? (Yes.) Even if they know nothing about maths? (Yes.) That's because ergodicity is an important idea with so many practical applications. Sadly, most books describe it in a very technical way, making it inaccessible to most people. In this short book, 6-times author Luca Dellanna describes ergodicity as simply as possible. You will read stories about how not knowing about it destroyed his cousin’s career as a skier, or how misunderstanding it caused additional deaths during the pandemic. You will learn how to spot situations in which ergodicity matters and the three strategies to react appropriately. The book is approximately 169 pages long, of which 143 are pure content and the rest tables of content, etc. Who is this book for? This book is for readers interested in growing themselves, their career, or their business, and who want to learn about ergodicity and its practical applications without having to understand its mathematical foundation. No mathematical knowledge is required, only a high-school level understanding of English. Readers who want to master the theory and mathematical foundation of ergodicity are better off reading a more formal manuscript. This book is not a substitute for it, but a complement. About the author Luca Dellanna is the author of 6 books. He is a researcher in complexity science and emergent behaviors, and an operational excellence consultant. He spoke at Nudgestock and regularly teaches risk management in masters. His personal website is Luca-Dellanna.com and his Twitter is @DellAnnaLuca.

Ergodicity

Author: Luca Dellanna

Publisher:

Published: 2021-02-18

Total Pages: 167

ISBN-13:

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Some reviews of this book, from Goodreads: "This is one of the most important books I've read, period. It's short, articulate and expansive on a singular subject matter -- ergodicity which is really the key ingredient to success in life, marriage, business, family, happiness, health, etc.. It's mathematical in origin but ubiquitous in application. High performance only matters if you survive." - Blake Janover "To not spent time and money on books that you should not waste resources on, please first read this book. This is a great book for those who quickly want to familiarize themselves with the concept of ergodicity. The author goes to great lengths explaining the concept in easily understandable terms. He also offers several practical implications for navigating non-ergodic environments. Highly recommended!" - Auke Hunneman What is ergodicity, and why does it matter? "The Most Important Property to Understand in Probability, in Life, in Anything." - Nassim Nicholas Taleb on ergodicity. "I think the most under-rated idea is ergodicity." - David Perell, author. Is ergodicity the most important concept in decision-making and behavioral sciences? (Yes.) Is it relevant for you in your daily life? (Yes.) Is it possible to explain it so simply that a grandma or a high-schooler can understand it? (Yes.) Even if they know nothing about maths? (Yes.) That's because ergodicity is an important idea with so many practical applications. Sadly, most books describe it in a very technical way, making it inaccessible to most people. In this short book, 6-times author Luca Dellanna describes ergodicity as simply as possible. You will read stories about how not knowing about it destroyed his cousin's career as a skier, or how misunderstanding it caused additional deaths during the pandemic. You will learn how to spot situations in which ergodicity matters and the three strategies to react appropriately. The book is approximately 169 pages long, of which 143 are pure content and the rest tables of content, etc. Who is this book for? This book is for readers interested in growing themselves, their career, or their business, and who want to learn about ergodicity and its practical applications without having to understand its mathematical foundation. No mathematical knowledge is required, only a high-school level understanding of English. Readers who want to master the theory and mathematical foundation of ergodicity are better off reading a more formal manuscript. This book is not a substitute for it, but a complement. About the author Luca Dellanna is the author of 6 books. He is a researcher in complexity science and emergent behaviors, and an operational excellence consultant. He spoke at Nudgestock and regularly teaches risk management in masters. His personal website is Luca-Dellanna.com and his Twitter is @DellAnnaLuca.

Lectures on Ergodic Theory

Author: Paul R. Halmos

Publisher: Courier Dover Publications

Published: 2017-12-13

Total Pages: 113

ISBN-13: 0486814890

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This concise classic by Paul R. Halmos, a well-known master of mathematical exposition, has served as a basic introduction to aspects of ergodic theory since its first publication in 1956. "The book is written in the pleasant, relaxed, and clear style usually associated with the author," noted the Bulletin of the American Mathematical Society, adding, "The material is organized very well and painlessly presented." Suitable for advanced undergraduates and graduate students in mathematics, the treatment covers recurrence, mean and pointwise convergence, ergodic theorem, measure algebras, and automorphisms of compact groups. Additional topics include weak topology and approximation, uniform topology and approximation, invariant measures, unsolved problems, and other subjects.

The Ergodic Theory of Discrete Sample Paths

Author: Paul C. Shields

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 263

ISBN-13: 0821804774

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This book is about finite-alphabet stationary processes, which are important in physics, engineering, and data compression. The focus is on the combinatorial properties of typical finite sample paths drawn from a stationary, ergodic process. A primary goal, only partially realized, is to develop a theory based directly on sample path arguments with minimal appeals to the probability formalism. A secondary goal is to give a careful presentation of the many models for stationary finite-alphabet processes that have been developed in probability theory, ergodic theory, and information theory.

Foundations of Ergodic Theory

Author: Marcelo Viana

Publisher: Cambridge University Press

Published: 2016-02-15

Total Pages: 547

ISBN-13: 1316445429

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Rich with examples and applications, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. The authors' clear and fluent exposition helps the reader to grasp quickly the most important ideas of the theory, and their use of concrete examples illustrates these ideas and puts the results into perspective. The book requires few prerequisites, with background material supplied in the appendix. The first four chapters cover elementary material suitable for undergraduate students – invariance, recurrence and ergodicity – as well as some of the main examples. The authors then gradually build up to more sophisticated topics, including correlations, equivalent systems, entropy, the variational principle and thermodynamical formalism. The 400 exercises increase in difficulty through the text and test the reader's understanding of the whole theory. Hints and solutions are provided at the end of the book.

Function Theory of One Complex Variable

Author: Robert Everist Greene

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 536

ISBN-13: 9780821839621

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Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples andexercises that illustrate this point. The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem,and the Bergman kernel. The authors also treat $Hp$ spaces and Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.

Ergodic Theory and Fractal Geometry

Author: Hillel Furstenberg

Publisher: American Mathematical Society

Published: 2014-08-08

Total Pages: 82

ISBN-13: 1470410346

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Fractal geometry represents a radical departure from classical geometry, which focuses on smooth objects that "straighten out" under magnification. Fractals, which take their name from the shape of fractured objects, can be characterized as retaining their lack of smoothness under magnification. The properties of fractals come to light under repeated magnification, which we refer to informally as "zooming in". This zooming-in process has its parallels in dynamics, and the varying "scenery" corresponds to the evolution of dynamical variables. The present monograph focuses on applications of one branch of dynamics--ergodic theory--to the geometry of fractals. Much attention is given to the all-important notion of fractal dimension, which is shown to be intimately related to the study of ergodic averages. It has been long known that dynamical systems serve as a rich source of fractal examples. The primary goal in this monograph is to demonstrate how the minute structure of fractals is unfolded when seen in the light of related dynamics. A co-publication of the AMS and CBMS.

Random Seas And Design Of Maritime Structures (3rd Edition)

Author: Goda Yoshimi

Publisher: World Scientific Publishing Company

Published: 2010-06-23

Total Pages: 732

ISBN-13: 9813101024

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Random waves are the most important constituent of the sea environment, as they make the design of maritime structures quite different from that of structures on land. In this book, the concept of random waves for the design of breakwaters, seawalls, and harbor structures is fully explored for easy comprehension by practicing engineers. Theoretical aspects are also discussed in detail for further studies by graduate students and researchers.

Counterexamples in Probability

Author: Jordan M. Stoyanov

Publisher: Courier Corporation

Published: 2014-01-15

Total Pages: 368

ISBN-13: 0486499987

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"While most mathematical examples illustrate the truth of a statement, counterexamples demonstrate a statement's falsity. Enjoyable topics of study, counterexamples are valuable tools for teaching and learning. The definitive book on the subject in regards to probability, this third edition features the author's revisions and corrections plus a substantial new appendix. 2013 edition"--

Probability, Random Processes, and Ergodic Properties

Author: Robert M. Gray

Publisher: Springer Science & Business Media

Published: 2013-04-18

Total Pages: 309

ISBN-13: 1475720246

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This book has been written for several reasons, not all of which are academic. This material was for many years the first half of a book in progress on information and ergodic theory. The intent was and is to provide a reasonably self-contained advanced treatment of measure theory, prob ability theory, and the theory of discrete time random processes with an emphasis on general alphabets and on ergodic and stationary properties of random processes that might be neither ergodic nor stationary. The intended audience was mathematically inc1ined engineering graduate students and visiting scholars who had not had formal courses in measure theoretic probability . Much of the material is familiar stuff for mathematicians, but many of the topics and results have not previously appeared in books. The original project grew too large and the first part contained much that would likely bore mathematicians and dis courage them from the second part. Hence I finally followed the suggestion to separate the material and split the project in two. The original justification for the present manuscript was the pragmatic one that it would be a shame to waste all the effort thus far expended. A more idealistic motivation was that the presentation bad merit as filling a unique, albeit smaIl, hole in the literature.