Percolation theory for mathematicians:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1982
Springer Scienc, Business Media, LLC |
| Schriftenreihe: | Progress in probability and statistics
Vol. 2 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000113479&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | 423 Seiten Illustrationen |
| ISBN: | 3764331070 9780817631079 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV000194360 | ||
| 003 | DE-604 | ||
| 005 | 20240911 | ||
| 007 | t| | ||
| 008 | 870612s1982 xx a||| |||| 00||| eng d | ||
| 020 | |a 3764331070 |9 3-7643-3107-0 | ||
| 020 | |a 9780817631079 |9 978-0-8176-3107-9 | ||
| 035 | |a (OCoLC)230593639 | ||
| 035 | |a (DE-599)BVBBV000194360 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-384 |a DE-739 |a DE-355 |a DE-824 |a DE-29T |a DE-91G |a DE-703 |a DE-19 |a DE-706 |a DE-634 |a DE-83 |a DE-11 |a DE-188 | ||
| 084 | |a SK 170 |0 (DE-625)143221: |2 rvk | ||
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 084 | |a PHY 602f |2 stub | ||
| 084 | |a 82A05 |2 msc/1980 | ||
| 100 | 1 | |a Kesten, Harry |d 1931-2019 |0 (DE-588)121449300 |4 aut | |
| 245 | 1 | 0 | |a Percolation theory for mathematicians |c Harry Kesten |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1982 | |
| 264 | 1 | |b Springer Scienc, Business Media, LLC | |
| 300 | |a 423 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in probability and statistics |v Vol. 2 | |
| 650 | 0 | 7 | |a Perkolationstheorie |0 (DE-588)4323583-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Methode |0 (DE-588)4155620-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Perkolation |0 (DE-588)4115530-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Statistische Physik |0 (DE-588)4057000-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Perkolationstheorie |0 (DE-588)4323583-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Perkolation |0 (DE-588)4115530-0 |D s |
| 689 | 1 | 1 | |a Mathematische Methode |0 (DE-588)4155620-3 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Perkolation |0 (DE-588)4115530-0 |D s |
| 689 | 2 | 1 | |a Statistische Physik |0 (DE-588)4057000-9 |D s |
| 689 | 2 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4899-2730-9 |
| 830 | 0 | |a Progress in probability and statistics |v Vol. 2 |w (DE-604)BV000010596 |9 2 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000113479&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-000113479 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 PHY 050f 2001 A 20548 |
|---|---|
| DE-BY-TUM_katkey | 815596 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020359944 |
| _version_ | 1821931026619826176 |
| adam_text | TABLE OF CONTENTS
1. Introduction and summary. 1
2. Which graphs do we consider? 10
2.1 Periodic graphs. 10
2.2 Matching pairs. 16
2.3 Planar modifications of matching pairs. 21
2.4 Separation theorems and related point set topological
results. 29
2.5 Covering graphs. 36
2.6 Dual graphs. 37
3. Periodic percolation problems. 40
3.1 Introduction of probability. Site vs bond problems. 40
3.2 Periodic site percolation. 44
3.3 Crossing probabilities and the principal theorem on
percolative regions. 46
3.4 Critical probabilities. Applications of the principal
theorems. 51
4. Increasing events. 69
4.1 The FKG inequality. 72
4.2 Pivotal sites and Russo s formula. 74
5. Bounds for the distribution of #W. 81
5.1 Exponential fall off of P{#W _ n). 83
5.2 Estimates above the percolation threshold. 97
5.3 Large crossing probabilities imply that percolation
occurs. 121
6. The RSW Theorem. 126
7. Proofs of Theorems 3.1 and 3.2. 168
8. Power estimates. 198
9. The nature of the singularity at p^. 238
10. Inequalities for critical probabilities. 255
10.1 Comparison of bond and site problems. 256
10.2 Strict inequality for a graph and a subgraph. 261
10.3 Derivation of Condition E from Condition D. 295
11. Resistance of random electrical networks. 335
11.1 Bounds for resistances of networks. 335
11.2 Proof of Theorem 11.1. 343
11.3 Properties of resistances. 351
11.4 Proofs of Theorems 11.2 and 11.3. 371
12. Unsolved problems. 380
Appendix. 386
References. 413
Author index. 418
Subject index. 419
Index of symbols. 421
|
| any_adam_object | 1 |
| author | Kesten, Harry 1931-2019 |
| author_GND | (DE-588)121449300 |
| author_facet | Kesten, Harry 1931-2019 |
| author_role | aut |
| author_sort | Kesten, Harry 1931-2019 |
| author_variant | h k hk |
| building | Verbundindex |
| bvnumber | BV000194360 |
| classification_rvk | SK 170 SK 820 SK 950 |
| classification_tum | PHY 602f |
| ctrlnum | (OCoLC)230593639 (DE-599)BVBBV000194360 |
| discipline | Physik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02209nam a2200529 cb4500</leader><controlfield tag="001">BV000194360</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20240911 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">870612s1982 xx a||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3764331070</subfield><subfield code="9">3-7643-3107-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780817631079</subfield><subfield code="9">978-0-8176-3107-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)230593639</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV000194360</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-12</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 170</subfield><subfield code="0">(DE-625)143221:</subfield><subfield code="2">rvk</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">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHY 602f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">82A05</subfield><subfield code="2">msc/1980</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kesten, Harry</subfield><subfield code="d">1931-2019</subfield><subfield code="0">(DE-588)121449300</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Percolation theory for mathematicians</subfield><subfield code="c">Harry Kesten</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston [u.a.]</subfield><subfield code="b">Birkhäuser</subfield><subfield code="c">1982</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="b">Springer Scienc, Business Media, LLC</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">423 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">Progress in probability and statistics</subfield><subfield code="v">Vol. 2</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Perkolationstheorie</subfield><subfield code="0">(DE-588)4323583-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematische Methode</subfield><subfield code="0">(DE-588)4155620-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Perkolation</subfield><subfield code="0">(DE-588)4115530-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Statistische Physik</subfield><subfield code="0">(DE-588)4057000-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Perkolationstheorie</subfield><subfield code="0">(DE-588)4323583-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Perkolation</subfield><subfield code="0">(DE-588)4115530-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Mathematische Methode</subfield><subfield code="0">(DE-588)4155620-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Perkolation</subfield><subfield code="0">(DE-588)4115530-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="1"><subfield code="a">Statistische Physik</subfield><subfield code="0">(DE-588)4057000-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</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">978-1-4899-2730-9</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Progress in probability and statistics</subfield><subfield code="v">Vol. 2</subfield><subfield code="w">(DE-604)BV000010596</subfield><subfield code="9">2</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</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=000113479&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:BVB01-000113479</subfield></datafield></record></collection> |
| id | DE-604.BV000194360 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T07:17:05Z |
| institution | BVB |
| isbn | 3764331070 9780817631079 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000113479 |
| oclc_num | 230593639 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-91G DE-BY-TUM DE-703 DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-12 DE-384 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-91G DE-BY-TUM DE-703 DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | 423 Seiten Illustrationen |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Birkhäuser Springer Scienc, Business Media, LLC |
| record_format | marc |
| series | Progress in probability and statistics |
| series2 | Progress in probability and statistics |
| spellingShingle | Kesten, Harry 1931-2019 Percolation theory for mathematicians Progress in probability and statistics Perkolationstheorie (DE-588)4323583-9 gnd Mathematische Methode (DE-588)4155620-3 gnd Perkolation (DE-588)4115530-0 gnd Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4323583-9 (DE-588)4155620-3 (DE-588)4115530-0 (DE-588)4057000-9 |
| title | Percolation theory for mathematicians |
| title_auth | Percolation theory for mathematicians |
| title_exact_search | Percolation theory for mathematicians |
| title_full | Percolation theory for mathematicians Harry Kesten |
| title_fullStr | Percolation theory for mathematicians Harry Kesten |
| title_full_unstemmed | Percolation theory for mathematicians Harry Kesten |
| title_short | Percolation theory for mathematicians |
| title_sort | percolation theory for mathematicians |
| topic | Perkolationstheorie (DE-588)4323583-9 gnd Mathematische Methode (DE-588)4155620-3 gnd Perkolation (DE-588)4115530-0 gnd Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Perkolationstheorie Mathematische Methode Perkolation Statistische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000113479&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000010596 |
| work_keys_str_mv | AT kestenharry percolationtheoryformathematicians |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 PHY 050f 2001 A 20548
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |