TY - BOOK

T1 - Probability

T2 - The classical limit theorems

AU - McKean, Henry

N1 - Publisher Copyright:
© Henry McKean 2014.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84952923360&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84952923360&partnerID=8YFLogxK

U2 - 10.1017/CBO9781107282032

DO - 10.1017/CBO9781107282032

M3 - Book

AN - SCOPUS:84952923360

SN - 9781107053212

BT - Probability

PB - Cambridge University Press

ER -