Probability: The Classical Limit Theorems

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Henry McKeanCambridge University Press, 7/31/2014EAN 9781107628274, ISBN10: 110762827XPaperback, 490 pages, 22.8 x 15.2 x 2.3 cmLanguage: EnglishProbability theory has been extraor dinarily successful at describing a variety of phenomena, from the behaviour of gases to the transmission of messages, and is, besides, a powerful tool with applications throughout mathematics. At its heart are a number of concepts familiar in one guise or another to many: Gauss' bell-shaped curve, the law of averages, and so on, concepts that crop up in so many settings they are in some sense universal. This universality is predicted by probability theory to a remarkable degree. 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.Preface1. Preliminaries2. Bernoulli trials3. The standard random walk4. The standard random walk in higher dimensions5. LLN, CLT, iterated log, and arcsine in general6. Brownian motion7. Markov chains8. The ergodic theorem9. Communication over a noisy channel10. Equilibrium statistical mechanics11. Statistical mechanics out of equilibrium12. Random matricesBibliographyIndex. Show more