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."
General
| Imprint: |
Springer-Verlag New York
|
| Country of origin: |
United States |
| Series: |
Applied Mathematical Sciences, 77 |
| Release date: |
December 2010 |
| First published: |
1989 |
| Authors: |
David Aldous
|
| Dimensions: |
235 x 155 x 15mm (L x W x T) |
| Format: |
Paperback
|
| Pages: |
272 |
| Edition: |
Softcover reprint of hardcover 1st ed. 1989 |
| ISBN-13: |
978-1-4419-3088-0 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Probability & statistics
Promotions
|
| LSN: |
1-4419-3088-4 |
| Barcode: |
9781441930880 |
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