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Field name	Details
Dewey Class	519.2
Title	Probability Approximations via the Poisson Clumping Heuristic ([EBook]) / by David Aldous
Author	Aldous, David J.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer New York , 1989
Physical Details	XVI, 272 p. : online resource.
Series	Applied mathematical sciences 0066-5452 ; ; 77
ISBN	9781475762839
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4757-6283-9
Links to Related Works	Subject References: Mathematics . Probabilities . Probability theory and stochastic processes . Authors: Aldous, David J. . Corporate Authors: SpringerLink (Online service) . Series: Applied mathematical sciences . Classification: 519.2 .

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Probability Approximations via the Poisson Clumping Heuristic

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