First steps in random walks: from tools to applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2011
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | VI, 152 S. Ill., graph. Darst. |
| ISBN: | 9780199234868 9780198754091 |
Internformat
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| 245 | 1 | 0 | |a First steps in random walks |b from tools to applications |c J. Klafter and I. M. Sokolov |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2011 | |
| 300 | |a VI, 152 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804148401072242688 |
|---|---|
| adam_text | Titel: First steps in random walks
Autor: Klafter, Joseph
Jahr: 2011
Contents
Abbreviations vii
1 Characteristic functions 1
1.1 First example: A random walk on a one-dimensional lattice 2
1.2 More general considerations 4
1.3 The moments 6
1.4 Random walk as a process with independent increments 6
1.5 A pedestrian approach to the Central Limit Theorem 7
1.6 When the Central Limit Theorem breaks down 10
1.7 Random walks in higher dimensions 13
2 Generating functions and applications 17
2.1 Definitions and properties 17
2.2 Tauberian theorems 19
2.3 Application to random walks: The first-passage and return
probabilities 21
2.4 Mean number of distinct visited sites 27
2.5 Sparre Andersen theorem 29
3 Continuous-time random walks 36
3.1 Waiting-time distributions 36
3.2 Transforming steps into time 39
3.3 Moments of displacement in CTRW 42
3.4 Power-law waiting-time distributions 43
3.5 Mean number of steps, MSD, and probability of being at the origin 49
3.6 Other characteristic properties of heavy-tailed CTRW 51
4 CTRW and aging phenomena 54
4.1 When the process ages 54
4.2 Forward waiting time 55
4.3 PDF of the walker s positions 60
4.4 Moving time averages 62
4.5 Response to the time-dependent field 65
5 Master equations 68
5.1 A heuristic derivation of the generalized master equation 70
5.2 A note on time-dependent transition probabilities 74
5.3 Relation between the solutions to the generalized and the
customary master equations 75
5.4 Generalized Fokker-Planck and diffusion equations 77
6 Fractional diffusion and Fokker-Planck equations for subdiffusion 80
6.1 Riemann-Liouville and Weyl derivatives 80
6.2 Griinwald-Letnikov representation 83
6.3 Fractional diffusion equation 84
6.4 Eigenfunction expansion 89
6.5 Subordination and the forms of the PDFs 92
7 Levy flights 97
7.1 General Levy distributions 98
7.2 Space-fractional diffusion equation for Levy flights 102
7.3 Leapover 104
7.4 Simulation of Levy distributions 106
8 Coupled CTRW and Levy walks 110
8.1 Space-time coupled CTRWs 110
8.2 Levy walks 114
8.3 Levy walk interrupted by rests 119
9 Simple reactions: A + B - B 123
9.1 Configurational averaging 123
9.2 A target problem 125
9.3 Trapping problem 127
9.4 Asymptotics of trapping kinetics in one dimension 129
9.5 Trapping in higher dimensions 132
10 Random walks on percolation structures 135
10.1 Some facts about percolation 137
10.2 Fractals 139
10.3 Random walks on fractals 141
10.4 Calculating the spectral dimension 143
10.5 Using the spectral dimension 145
10.6 The role of finite clusters 147
Index 151
|
| any_adam_object | 1 |
| author | Klafter, Joseph 1945- Sokolov, Igor M. 1958- |
| author_GND | (DE-588)1020323450 (DE-588)138533199 |
| author_facet | Klafter, Joseph 1945- Sokolov, Igor M. 1958- |
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| author_sort | Klafter, Joseph 1945- |
| author_variant | j k jk i m s im ims |
| building | Verbundindex |
| bvnumber | BV039573191 |
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| dewey-full | 519.282 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-search | 519.282 |
| dewey-sort | 3519.282 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV039573191 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:06:33Z |
| institution | BVB |
| isbn | 9780199234868 9780198754091 |
| language | English |
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| physical | VI, 152 S. Ill., graph. Darst. |
| publishDate | 2011 |
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| spelling | Klafter, Joseph 1945- Verfasser (DE-588)1020323450 aut First steps in random walks from tools to applications J. Klafter and I. M. Sokolov 1. publ. Oxford [u.a.] Oxford Univ. Press 2011 VI, 152 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Irrfahrtsproblem (DE-588)4162442-7 gnd rswk-swf Irrfahrtsproblem (DE-588)4162442-7 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Sokolov, Igor M. 1958- Verfasser (DE-588)138533199 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024424662&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Klafter, Joseph 1945- Sokolov, Igor M. 1958- First steps in random walks from tools to applications Stochastischer Prozess (DE-588)4057630-9 gnd Irrfahrtsproblem (DE-588)4162442-7 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4162442-7 |
| title | First steps in random walks from tools to applications |
| title_auth | First steps in random walks from tools to applications |
| title_exact_search | First steps in random walks from tools to applications |
| title_full | First steps in random walks from tools to applications J. Klafter and I. M. Sokolov |
| title_fullStr | First steps in random walks from tools to applications J. Klafter and I. M. Sokolov |
| title_full_unstemmed | First steps in random walks from tools to applications J. Klafter and I. M. Sokolov |
| title_short | First steps in random walks |
| title_sort | first steps in random walks from tools to applications |
| title_sub | from tools to applications |
| topic | Stochastischer Prozess (DE-588)4057630-9 gnd Irrfahrtsproblem (DE-588)4162442-7 gnd |
| topic_facet | Stochastischer Prozess Irrfahrtsproblem |
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