Probability

The Classical Limit Theorems

Henry McKean (Autor)

Buch | Softcover

490 Seiten

2014
Cambridge University Press (Verlag)
978-1-107-62827-4 (ISBN)

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Probability theory is explained here by one of its leading authorities. McKean constructs a clear path through the subject and sheds light on a variety of interesting topics in which probability theory plays a key role. Anyone who wants to learn or use probability will benefit from reading this book.

Probability theory has been extraordinarily 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.

Henry McKean is a professor in the Courant Institute of Mathematical Sciences at New York University. He is a fellow of the American Mathematical Society and in 2007 he received the Leroy P. Steele Prize for his life's work.

Preface; 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.

Zusatzinfo	Worked examples or Exercises; 2 Halftones, unspecified; 120 Line drawings, unspecified
Verlagsort	Cambridge
Sprache	englisch
Maße	152 x 228 mm
Gewicht	760 g
Themenwelt	Mathematik / Informatik ► Informatik ► Netzwerke
	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
ISBN-10	1-107-62827-X / 110762827X
ISBN-13	978-1-107-62827-4 / 9781107628274
Zustand	Neuware