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Probability Approximations via the Poisson Clumping Heuristic

  • Book
  • © 1989

Overview

Authors:
  1. David Aldous

    1. Department of Statistics, University of California-Berkeley, Berkeley, USA

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Part of the book series: Applied Mathematical Sciences (AMS, volume 77)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xv
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  2. The Heuristic

    • David Aldous
    Pages 1-22

  3. Markov Chain Hitting Times

    • David Aldous
    Pages 23-43

  4. Extremes of Stationary Processes

    • David Aldous
    Pages 44-71

  5. Extremes of Locally Brownian Processes

    • David Aldous
    Pages 72-105

  6. Simple Combinatorics

    • David Aldous
    Pages 106-117

  7. Combinatorics for Processes

    • David Aldous
    Pages 118-130

  8. Exponential Combinatorial Extrema

    • David Aldous
    Pages 131-148

  9. Stochastic Geometry

    • David Aldous
    Pages 149-166

  10. Multi-Dimensional Diffusions

    • David Aldous
    Pages 167-189

  11. Random Fields

    • David Aldous
    Pages 190-219

  12. Brownian Motion: Local Distributions

    • David Aldous
    Pages 220-236

  13. Miscellaneous Examples

    • David Aldous
    Pages 237-245

  14. The Eigenvalue Method

    • David Aldous
    Pages 246-251

  15. Postscript

    • David Aldous
    Pages 252-252

  16. Back Matter

    Pages 253-271
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Keywords

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 min­ ima, in some sense.

Authors and Affiliations

  • Department of Statistics, University of California-Berkeley, Berkeley, USA

    David Aldous

Bibliographic Information

  • Book Title: Probability Approximations via the Poisson Clumping Heuristic

  • Authors: David Aldous

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4757-6283-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1989

  • Hardcover ISBN: 978-0-387-96899-5Published: 14 November 1988

  • Softcover ISBN: 978-1-4419-3088-0Published: 01 December 2010

  • eBook ISBN: 978-1-4757-6283-9Published: 09 March 2013

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: XVI, 272

  • Topics: Probability Theory and Stochastic Processes

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