Probability Approximations via the Poisson Clumping Heuristic (eBook, PDF)
David Aldous
eBook, PDF

Probability Approximations via the Poisson Clumping Heuristic (eBook, PDF)

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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 ...

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