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Probability : the classical limit theorems / Henry Mckean.

By: Material type: TextTextPublication details: Cambridge : Cambridge University Press, 2014.Description: xxi, 464 p. : illustrations ; 24 cmISBN:
  • 9781107053212 (hardback)
Subject(s): DDC classification:
  • 519.2 23 M154
Contents:
1. Preliminaries -- 2. Bernoulli trials -- 3. The standard random walk -- 4. The standard random walk in higher dimensions -- 5. LLN, CLT, iterated log, and arcsine in general -- 6. Brownian motion -- 7. Markov chains -- 8. The ergodic theorem -- 9. Communication over a noisy channel -- 10. Equilibrium statistical mechanics -- 11. Statistical mechanics out of equilibrium -- 12. Random matrices-- Bibliography-- Index.
Summary: This book explains that theory and investigates its ramifications. Assuming a good working knowledge of basic analysis, real and complex, the author maps out a route from basic probability, via random walks, Brownian motion, the law of large numbers and the central limit theorem, to aspects of ergodic theorems, equilibrium and nonequilibrium statistical mechanics, communication over a noisy channel, and random matrices. Numerous examples and exercises enrich the text.
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Includes bibliographical references and index.

1. Preliminaries --
2. Bernoulli trials --
3. The standard random walk --
4. The standard random walk in higher dimensions --
5. LLN, CLT, iterated log, and arcsine in general --
6. Brownian motion --
7. Markov chains --
8. The ergodic theorem --
9. Communication over a noisy channel --
10. Equilibrium statistical mechanics --
11. Statistical mechanics out of equilibrium --
12. Random matrices--
Bibliography--
Index.

This book explains that theory and investigates its ramifications. Assuming a good working knowledge of basic analysis, real and complex, the author maps out a route from basic probability, via random walks, Brownian motion, the law of large numbers and the central limit theorem, to aspects of ergodic theorems, equilibrium and nonequilibrium statistical mechanics, communication over a noisy channel, and random matrices. Numerous examples and exercises enrich the text.

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