Applied Mathematical Sciences

Probability Approximations via the Poisson Clumping Heuristic

Authors: Aldous, David

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About this book

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 minĀ­ ima, in some sense.

Table of contents (14 chapters)

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-1-4757-6283-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-0-387-96899-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.00
price for USA
  • ISBN 978-1-4419-3088-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Probability Approximations via the Poisson Clumping Heuristic
Authors
Series Title
Applied Mathematical Sciences
Series Volume
77
Copyright
1989
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-6283-9
DOI
10.1007/978-1-4757-6283-9
Hardcover ISBN
978-0-387-96899-5
Softcover ISBN
978-1-4419-3088-0
Series ISSN
0066-5452
Edition Number
1
Number of Pages
XVI, 272
Topics