Probability Approximations via the Poisson Clumping Heuristic:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1989
|
| Schriftenreihe: | Applied Mathematical Sciences
77 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XVI, 272 p) |
| ISBN: | 9781475762839 9781441930880 |
| ISSN: | 0066-5452 |
| DOI: | 10.1007/978-1-4757-6283-9 |
Internformat
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| author | Aldous, David |
| author_facet | Aldous, David |
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| author_variant | d a da |
| building | Verbundindex |
| bvnumber | BV042421687 |
| classification_tum | MAT 000 |
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| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-6283-9 |
| format | Electronic eBook |
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| id | DE-604.BV042421687 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475762839 9781441930880 |
| issn | 0066-5452 |
| language | English |
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| spelling | Aldous, David Verfasser aut Probability Approximations via the Poisson Clumping Heuristic by David Aldous New York, NY Springer New York 1989 1 Online-Ressource (XVI, 272 p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 77 0066-5452 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 Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 gnd rswk-swf Poisson-Prozess (DE-588)4174971-6 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Stochastische Geometrie (DE-588)4133202-7 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Kombinatorik (DE-588)4031824-2 s Stochastischer Prozess (DE-588)4057630-9 s 1\p DE-604 Poisson-Prozess (DE-588)4174971-6 s Approximation (DE-588)4002498-2 s 2\p DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 3\p DE-604 Stochastische Geometrie (DE-588)4133202-7 s 4\p DE-604 Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 s 5\p DE-604 Markov-Prozess (DE-588)4134948-9 s 6\p DE-604 https://doi.org/10.1007/978-1-4757-6283-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Aldous, David Probability Approximations via the Poisson Clumping Heuristic Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Approximation (DE-588)4002498-2 gnd Markov-Prozess (DE-588)4134948-9 gnd Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 gnd Poisson-Prozess (DE-588)4174971-6 gnd Kombinatorik (DE-588)4031824-2 gnd Stochastische Geometrie (DE-588)4133202-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4002498-2 (DE-588)4134948-9 (DE-588)4132446-8 (DE-588)4174971-6 (DE-588)4031824-2 (DE-588)4133202-7 (DE-588)4057630-9 |
| title | Probability Approximations via the Poisson Clumping Heuristic |
| title_auth | Probability Approximations via the Poisson Clumping Heuristic |
| title_exact_search | Probability Approximations via the Poisson Clumping Heuristic |
| title_full | Probability Approximations via the Poisson Clumping Heuristic by David Aldous |
| title_fullStr | Probability Approximations via the Poisson Clumping Heuristic by David Aldous |
| title_full_unstemmed | Probability Approximations via the Poisson Clumping Heuristic by David Aldous |
| title_short | Probability Approximations via the Poisson Clumping Heuristic |
| title_sort | probability approximations via the poisson clumping heuristic |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Approximation (DE-588)4002498-2 gnd Markov-Prozess (DE-588)4134948-9 gnd Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 gnd Poisson-Prozess (DE-588)4174971-6 gnd Kombinatorik (DE-588)4031824-2 gnd Stochastische Geometrie (DE-588)4133202-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Wahrscheinlichkeitsrechnung Approximation Markov-Prozess Kombinatorische Wahrscheinlichkeitstheorie Poisson-Prozess Kombinatorik Stochastische Geometrie Stochastischer Prozess |
| url | https://doi.org/10.1007/978-1-4757-6283-9 |
| work_keys_str_mv | AT aldousdavid probabilityapproximationsviathepoissonclumpingheuristic |