Fr. 157.00

Probability Approximations via the Poisson Clumping Heuristic

English · Paperback / Softback

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If you place a large number of points randomly in the unit square, what is the distribution of the radius of the largest circle containing no points? Of the smallest circle containing 4 points? Why do Brownian sample paths have local maxima but not points of increase, and how nearly do they have points of increase? Given two long strings of letters drawn i. i. d. from a finite alphabet, how long is the longest consecutive (resp. non-consecutive) substring appearing in both strings? If an imaginary particle performs a simple random walk on the vertices of a high-dimensional cube, how long does it take to visit every vertex? If a particle moves under the influence of a potential field and random perturbations of velocity, how long does it take to escape from a deep potential well? If cars on a freeway move with constant speed (random from car to car), what is the longest stretch of empty road you will see during a long journey? If you take a large i. i. d. sample from a 2-dimensional rotationally-invariant distribution, what is the maximum over all half-spaces of the deviation between the empirical and true distributions? These questions cover a wide cross-section of theoretical and applied probability. The common theme is that they all deal with maxima or min ima, in some sense.

List of contents

A The Heuristic.- B Markov Chain Hitting Times.- C Extremes of Stationary Processes.- D Extremes of Locally Brownian Processes.- E Simple Combinatorics.- F Combinatorics for Processes.- G Exponential Combinatorial Extrema.- H Stochastic Geometry.- I Multi-Dimensional Diffusions.- J Random Fields.- K Brownian Motion: Local Distributions.- L Miscellaneous Examples.- M The Eigenvalue Method.- Postscript.

Product details

Authors David Aldous
Publisher Springer, Berlin
 
Languages English
Product format Paperback / Softback
Released 27.10.2010
 
EAN 9781441930880
ISBN 978-1-4419-3088-0
No. of pages 272
Dimensions 154 mm x 17 mm x 239 mm
Weight 454 g
Illustrations XVI, 272 p.
Series Applied Mathematical Sciences
Applied Mathematical Sciences
Subject Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics

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