Probability

The classical limit theorems

Henry McKean

Research output: Book/ReportBook

Abstract

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.

Original languageEnglish (US)
PublisherCambridge University Press
Number of pages464
ISBN (Print)9781107282032, 9781107053212
DOIs
StatePublished - Jan 1 2014

Fingerprint

Classical Limit
Probability Theory
Limit Theorems
Bell curve
Nonequilibrium Statistical Mechanics
Ergodic Theorem
Law of large numbers
Ramification
Random Matrices
Central limit theorem
Exercise
Universality
Gauss
Brownian motion
Random walk
Concepts
Heart
Knowledge
Text
Gas

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Probability : The classical limit theorems. / McKean, Henry.

Cambridge University Press, 2014. 464 p.

Research output: Book/ReportBook

McKean, Henry. / Probability : The classical limit theorems. Cambridge University Press, 2014. 464 p.
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