Random walk: a modern introduction
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
[2010]
|
| Ausgabe: | First published |
| Schriftenreihe: | Cambridge studies in advanced mathematics
123 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020482662&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xii, 364 Seiten Illustrationen |
| ISBN: | 9780521519182 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV036561331 | ||
| 003 | DE-604 | ||
| 005 | 20240913 | ||
| 007 | t| | ||
| 008 | 100713s2010 xx a||| |||| 00||| eng d | ||
| 020 | |a 9780521519182 |c hardcover |9 978-0-521-51918-2 | ||
| 035 | |a (OCoLC)650629802 | ||
| 035 | |a (DE-599)BVBBV036561331 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-20 |a DE-11 |a DE-824 |a DE-703 |a DE-83 |a DE-91G |a DE-188 |a DE-19 | ||
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a 60G50 |2 msc/2000 | ||
| 084 | |a MAT 605f |2 stub | ||
| 100 | 1 | |a Lawler, Gregory F. |d 1955- |0 (DE-588)123908671 |4 aut | |
| 245 | 1 | 0 | |a Random walk |b a modern introduction |c Gregory F. Lawler ; Vlada Limic |
| 250 | |a First published | ||
| 264 | 1 | |a Cambridge |b Cambridge University Press |c [2010] | |
| 264 | 4 | |c © 2010 | |
| 300 | |a xii, 364 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge studies in advanced mathematics |v 123 | |
| 650 | 0 | 7 | |a Irrfahrtsproblem |0 (DE-588)4162442-7 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Irrfahrtsproblem |0 (DE-588)4162442-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Limic, Vlada |0 (DE-588)141817623 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-511-75085-4 |
| 830 | 0 | |a Cambridge studies in advanced mathematics |v 123 |w (DE-604)BV000003678 |9 123 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020482662&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-020482662 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 605 2010 A 8966 |
|---|---|
| DE-BY-TUM_katkey | 1746953 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010200498 040071475635 |
| _version_ | 1821933216758497281 |
| adam_text | Contents
Preface
page
ix
Introduction
1
1.1
Basic definitions
1
.2
Continuous-time random walk
6
.3
Other lattices
7
.4
Other walks
11
.5
Generator
11
.6
Filtrations and strong Markov property
14
.7
A word about constants
17
Local centra] limit theorem
21
2.1
Introduction
21
2.2
Characteristic functions and LCLT
25
2.2.1
Characteristic functions of random variables in M.d
25
2.2.2
Characteristic functions of random variables in Zd
27
2.3
LCLT
-
characteristic function approach
28
2.3.1
Exponential moments
46
2.4
Some corollaries of the LCLT
51
2.5
LCLT
-
combinatorial approach
58
2.5.1
Stirling s formula and one-dimensional walks
58
2.5.2
LCLT for
Poisson
and continuous-time walks
64
Approximation by Brow
nian
motion
72
3.1
Introduction
72
3.2
Construction of Brownian motion
74
3.3
Skorokhod embedding
79
3.4
Higher dimensions
82
3.5
An alternative formulation
84
vi
Contents
4
The Green s function
87
4.1
Recurrence and transience
87
4.2
The Green s generating function
88
4.3
The Green s function, transient case
95
4.3.1
Asymptotics under weaker assumptions
99
4.4
Potential kernel
101
4.4.1
Two dimensions
101
4.4.2
Asymptotics under weaker assumptions
107
4.4.3
One dimension
109
4.5
Fundamental solutions
113
4.6
The Green s function for a set
114
5
One-dimensional walks
123
5.1
Gambler s ruin estimate
123
5.1.1
General case
127
5.2
One-dimensional killed walks
135
5.3
Hitting a half-line
138
6
Potential theory
144
6.1
Introduction
144
6.2
Dirichlet problem
146
6.3
Difference estimates and Harnack inequality
152
6.4
Further estimates
160
6.5
Capacity, transient case
166
6.6
Capacity in two dimensions
176
6.7
Neumann problem
186
6.8
Beurling estimate
189
6.9
Eigenvalue of a set
194
7
Dyadic coupling
205
7.1
Introduction
205
7.2
Some estimates
207
7.3
Quantile coupling
210
7.4
The dyadic coupling
213
7.5
Proof of Theorem
7.1.1 216
7.6
Higher dimensions
218
7.7
Coupling the exit distributions
219
8
Additional topics on simple random walk
225
8.1
Poisson
kernel
225
8.1.1
Half space
226
Contents
vii
8.1.2
Cube
229
8.1.3 Strips
and quadrants in Z2
235
8.2
Eigenvalues for rectangles
238
8.3
Approximating continuous harmonic functions
239
8.4
Estimates for the ball
241
9
Loop measures
247
9.1
Introduction
247
9.2
Definitions and notations
247
9.2.1
Simple random walk on a graph
251
9.3
Generating functions and loop measures
252
9.4
Loop soup
257
9.5
Loop erasure
259
9.6
Boundary excursions
261
9.7
Wilson s algorithm and spanning trees
268
9.8
Examples
271
9.8.1
Complete graph
271
9.8.2
Hypercube
272
9.8.3
Sierpinski graphs
275
9.9
Spanning trees of subsets of Z2
277
9.10
Gaussian free field
289
10
Intersection probabilities for random walks
297
10.1
Long-range estimate
297
10.2
Short-range estimate
302
10.3
One-sided exponent
305
11
Loop-erased random walk
307
11.1
A-processes
307
11.2
Loop-erased random walk
311
11.3
LERWinZ^
313
11.3.1
d >3
314
11.3.2
d
=2 315
11.4
Rate of growth
319
11.5
Short-range intersections
323
Appendix
326
A.
1
Some expansions
326
A.
1.1
Riemann sums
326
A.
1.2
Logarithm
327
A.2 Martingales
331
A.2.
1
Optional sampling theorem
332
viii Contents
А.З
A.4
A.5
A.6
A.7
Bibliography
Index
с
Index
A.I.I Maximal inequality
334
A.
2.3
Continuous martingales
336
Joint normal distributions
337
Markov chains
339
A.4.
1
Chains restricted to subsets
342
A.4.
2
Maximal coupling of Markov chains
346
Some Tauberian theory
351
Second moment method
353
Subadditivity
354
iv
360
nbols
361
363
|
| any_adam_object | 1 |
| author | Lawler, Gregory F. 1955- Limic, Vlada |
| author_GND | (DE-588)123908671 (DE-588)141817623 |
| author_facet | Lawler, Gregory F. 1955- Limic, Vlada |
| author_role | aut aut |
| author_sort | Lawler, Gregory F. 1955- |
| author_variant | g f l gf gfl v l vl |
| building | Verbundindex |
| bvnumber | BV036561331 |
| classification_rvk | SK 820 |
| classification_tum | MAT 605f |
| ctrlnum | (OCoLC)650629802 (DE-599)BVBBV036561331 |
| discipline | Mathematik |
| edition | First published |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01725nam a2200421 cb4500</leader><controlfield tag="001">BV036561331</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20240913 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">100713s2010 xx a||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780521519182</subfield><subfield code="c">hardcover</subfield><subfield code="9">978-0-521-51918-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)650629802</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV036561331</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 820</subfield><subfield code="0">(DE-625)143258:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60G50</subfield><subfield code="2">msc/2000</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 605f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lawler, Gregory F.</subfield><subfield code="d">1955-</subfield><subfield code="0">(DE-588)123908671</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Random walk</subfield><subfield code="b">a modern introduction</subfield><subfield code="c">Gregory F. Lawler ; Vlada Limic</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">First published</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">[2010]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xii, 364 Seiten</subfield><subfield code="b">Illustrationen</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Cambridge studies in advanced mathematics</subfield><subfield code="v">123</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Irrfahrtsproblem</subfield><subfield code="0">(DE-588)4162442-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Irrfahrtsproblem</subfield><subfield code="0">(DE-588)4162442-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Limic, Vlada</subfield><subfield code="0">(DE-588)141817623</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-0-511-75085-4</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Cambridge studies in advanced mathematics</subfield><subfield code="v">123</subfield><subfield code="w">(DE-604)BV000003678</subfield><subfield code="9">123</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020482662&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-020482662</subfield></datafield></record></collection> |
| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV036561331 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:36:57Z |
| institution | BVB |
| isbn | 9780521519182 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020482662 |
| oclc_num | 650629802 |
| open_access_boolean | |
| owner | DE-20 DE-11 DE-824 DE-703 DE-83 DE-91G DE-BY-TUM DE-188 DE-19 DE-BY-UBM |
| owner_facet | DE-20 DE-11 DE-824 DE-703 DE-83 DE-91G DE-BY-TUM DE-188 DE-19 DE-BY-UBM |
| physical | xii, 364 Seiten Illustrationen |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spellingShingle | Lawler, Gregory F. 1955- Limic, Vlada Random walk a modern introduction Cambridge studies in advanced mathematics Irrfahrtsproblem (DE-588)4162442-7 gnd |
| subject_GND | (DE-588)4162442-7 (DE-588)4123623-3 |
| title | Random walk a modern introduction |
| title_auth | Random walk a modern introduction |
| title_exact_search | Random walk a modern introduction |
| title_full | Random walk a modern introduction Gregory F. Lawler ; Vlada Limic |
| title_fullStr | Random walk a modern introduction Gregory F. Lawler ; Vlada Limic |
| title_full_unstemmed | Random walk a modern introduction Gregory F. Lawler ; Vlada Limic |
| title_short | Random walk |
| title_sort | random walk a modern introduction |
| title_sub | a modern introduction |
| topic | Irrfahrtsproblem (DE-588)4162442-7 gnd |
| topic_facet | Irrfahrtsproblem Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020482662&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT lawlergregoryf randomwalkamodernintroduction AT limicvlada randomwalkamodernintroduction |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 605 2010 A 8966 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
| Exemplar 2 | Ausleihbar Am Standort |