Random graph dynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge series in statistical and probabilistic mathematics
[20] |
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents only Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references |
| Beschreibung: | IX, 212 S. graph. Darst. |
| ISBN: | 9780521866569 0521866561 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV021695031 | ||
| 003 | DE-604 | ||
| 005 | 20150814 | ||
| 007 | t | ||
| 008 | 060814s2007 xxud||| |||| 00||| eng d | ||
| 010 | |a 2006020925 | ||
| 020 | |a 9780521866569 |c hardback |9 978-0-521-86656-9 | ||
| 020 | |a 0521866561 |9 0-521-86656-1 | ||
| 035 | |a (OCoLC)70219882 | ||
| 035 | |a (DE-599)BVBBV021695031 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-91G |a DE-29T |a DE-83 |a DE-19 | ||
| 050 | 0 | |a QA166.17 | |
| 082 | 0 | |a 511/.5 | |
| 084 | |a SK 890 |0 (DE-625)143267: |2 rvk | ||
| 084 | |a 05C80 |2 msc | ||
| 084 | |a MAT 055f |2 stub | ||
| 100 | 1 | |a Durrett, Richard |d 1951- |e Verfasser |0 (DE-588)121396789 |4 aut | |
| 245 | 1 | 0 | |a Random graph dynamics |c Rick Durrett |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
| 300 | |a IX, 212 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge series in statistical and probabilistic mathematics |v [20] | |
| 500 | |a Includes bibliographical references | ||
| 650 | 7 | |a Dynamica |2 gtt | |
| 650 | 7 | |a Grafentheorie |2 gtt | |
| 650 | 4 | |a Graphes aléatoires | |
| 650 | 4 | |a Random graphs | |
| 650 | 0 | 7 | |a Zufallsgraph |0 (DE-588)4277661-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Zufallsgraph |0 (DE-588)4277661-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Cambridge series in statistical and probabilistic mathematics |v [20] |w (DE-604)BV011442366 |9 20 | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0661/2006020925-d.html |3 Publisher description | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0661/2006020925-t.html |3 Table of contents only | |
| 856 | 4 | 2 | |m HEBIS Datenaustausch Darmstadt |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014909048&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-014909048 | ||
Datensatz im Suchindex
| _version_ | 1804135523157016576 |
|---|---|
| adam_text | RANDOM GRAPH DYNAMICS RICK DURRETT CORNELL UNIVERSITY CAMBRIDGE
UNIVERSITY PRESS CONTENTS PREFACE PAGE VII 1. OVERVIEW 1 1.1
INTRODUCTION TO THE INTRODUCTION 1 1.2 ERDOS, RENYI, MOLLOY, AND REED 3
1.3 SIX DEGREES, SMALL WORLDS 7 1.4 POWER LAWS, PREFERENTIAL ATTACHMENT
11 1.5 EPIDEMICS AND PERCOLATION 15 1.6 POTTS MODELS AND THE CONTACT
PROCESS 18 1.7 RANDOM WALKS AND VOTER MODELS 20 1.8 CHKNS MODEL 21 2.
ERDOS-RENYI RANDOM GRAPHS 27 2.1 BRANCHING PROCESSES 27 2.2 CLUSTER
GROWTH AS AN EPIDEMIC 34 2.3 CLUSTER GROWTH AS A RANDOM WALK 37 2.4
DIAMETER OF THE GIANT COMPONENT 43 2.5 CLT FOR THE GIANT COMPONENT 46
2.6 COMBINATORIAL APPROACH 50 2.7 CRITICAL REGIME 56 2.8 THRESHOLD FOR
CONNECTIVITY 62 3. FIXED DEGREE DISTRIBUTIONS 70 3.1 DEFINITIONS AND
HEURISTICS 70 3.2 PROOF OF PHASE TRANSITION 75 3.3 SUBCRITICAL ESTIMATES
82 3.4 DISTANCES: FINITE VARIANCE 84 3.5 EPIDEMICS 85 4. POWER LAWS 90
4.1 BARABASI-ALBERT MODEL 90 4.2 RELATED MODELS 93 4.3 MARTINGALES AND
URNS 99 4.4 SCALE-FREE TREES 105 4.5 DISTANCES: POWER LAWS 2 FT 3
110 CONTENTS 4.6 DIAMETER: BARABASI-ALBERT MODEL 4.7 PERCOLATION,
RESILIENCE 4.8 SIS EPIDEMIC 5. SMALL WORLDS 5.1 WATTS AND STROGATZ MODEL
5.2 PATH LENGTHS 5.3 5.4 5.5 EPIDEMICS ISING AND POTTS MODELS CONTACT
PROCESS 6. RANDOM WALKS 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 SPECTRAL GAP
CONDUCTANCE FIXED DEGREE DISTRIBUTION PREFERENTIAL ATTACHMENT GRAPH
CONNECTED ERDOS-RENYI GRAPHS SMALL WORLDS ONLY DEGREES 2 AND 3 HITTING
TIMES VOTER MODELS 7. CHKNS MODEL 7.1 7.2 7.3 7.4 7.5 HEURISTIC
ARGUMENTS PROOF OF THE PHASE TRANSITION SUBCRITICAL ESTIMATES
KOSTERLITZ-THOULESS TRANSITION RESULTS AT THE CRITICAL VALUE REFERENCES
INDEX 116 121 125 132 132 134 140 144 148 153 153 156 159 164 169 171
175 177 181 187 187 190 193 197 200 203 211
|
| adam_txt |
RANDOM GRAPH DYNAMICS RICK DURRETT CORNELL UNIVERSITY CAMBRIDGE
UNIVERSITY PRESS CONTENTS PREFACE PAGE VII 1. OVERVIEW 1 1.1
INTRODUCTION TO THE INTRODUCTION 1 1.2 ERDOS, RENYI, MOLLOY, AND REED 3
1.3 SIX DEGREES, SMALL WORLDS 7 1.4 POWER LAWS, PREFERENTIAL ATTACHMENT
11 1.5 EPIDEMICS AND PERCOLATION 15 1.6 POTTS MODELS AND THE CONTACT
PROCESS 18 1.7 RANDOM WALKS AND VOTER MODELS 20 1.8 CHKNS MODEL 21 2.
ERDOS-RENYI RANDOM GRAPHS 27 2.1 BRANCHING PROCESSES 27 2.2 CLUSTER
GROWTH AS AN EPIDEMIC 34 2.3 CLUSTER GROWTH AS A RANDOM WALK 37 2.4
DIAMETER OF THE GIANT COMPONENT 43 2.5 CLT FOR THE GIANT COMPONENT 46
2.6 COMBINATORIAL APPROACH 50 2.7 CRITICAL REGIME 56 2.8 THRESHOLD FOR
CONNECTIVITY 62 3. FIXED DEGREE DISTRIBUTIONS 70 3.1 DEFINITIONS AND
HEURISTICS 70 3.2 PROOF OF PHASE TRANSITION 75 3.3 SUBCRITICAL ESTIMATES
82 3.4 DISTANCES: FINITE VARIANCE 84 3.5 EPIDEMICS 85 4. POWER LAWS 90
4.1 BARABASI-ALBERT MODEL 90 4.2 RELATED MODELS 93 4.3 MARTINGALES AND
URNS 99 4.4 SCALE-FREE TREES 105 4.5 DISTANCES: POWER LAWS 2 FT 3
110 CONTENTS 4.6 DIAMETER: BARABASI-ALBERT MODEL 4.7 PERCOLATION,
RESILIENCE 4.8 SIS EPIDEMIC 5. SMALL WORLDS 5.1 WATTS AND STROGATZ MODEL
5.2 PATH LENGTHS 5.3 5.4 5.5 EPIDEMICS ISING AND POTTS MODELS CONTACT
PROCESS 6. RANDOM WALKS 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 SPECTRAL GAP
CONDUCTANCE FIXED DEGREE DISTRIBUTION PREFERENTIAL ATTACHMENT GRAPH
CONNECTED ERDOS-RENYI GRAPHS SMALL WORLDS ONLY DEGREES 2 AND 3 HITTING
TIMES VOTER MODELS 7. CHKNS MODEL 7.1 7.2 7.3 7.4 7.5 HEURISTIC
ARGUMENTS PROOF OF THE PHASE TRANSITION SUBCRITICAL ESTIMATES
KOSTERLITZ-THOULESS TRANSITION RESULTS AT THE CRITICAL VALUE REFERENCES
INDEX 116 121 125 132 132 134 140 144 148 153 153 156 159 164 169 171
175 177 181 187 187 190 193 197 200 203 211 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Durrett, Richard 1951- |
| author_GND | (DE-588)121396789 |
| author_facet | Durrett, Richard 1951- |
| author_role | aut |
| author_sort | Durrett, Richard 1951- |
| author_variant | r d rd |
| building | Verbundindex |
| bvnumber | BV021695031 |
| callnumber-first | Q - Science |
| callnumber-label | QA166 |
| callnumber-raw | QA166.17 |
| callnumber-search | QA166.17 |
| callnumber-sort | QA 3166.17 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 890 |
| classification_tum | MAT 055f |
| ctrlnum | (OCoLC)70219882 (DE-599)BVBBV021695031 |
| dewey-full | 511/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.5 |
| dewey-search | 511/.5 |
| dewey-sort | 3511 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02015nam a2200517 cb4500</leader><controlfield tag="001">BV021695031</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20150814 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">060814s2007 xxud||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2006020925</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780521866569</subfield><subfield code="c">hardback</subfield><subfield code="9">978-0-521-86656-9</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521866561</subfield><subfield code="9">0-521-86656-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)70219882</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV021695031</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA166.17</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511/.5</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 890</subfield><subfield code="0">(DE-625)143267:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">05C80</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 055f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Durrett, Richard</subfield><subfield code="d">1951-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)121396789</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Random graph dynamics</subfield><subfield code="c">Rick Durrett</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge [u.a.]</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">IX, 212 S.</subfield><subfield code="b">graph. Darst.</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 series in statistical and probabilistic mathematics</subfield><subfield code="v">[20]</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Dynamica</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Grafentheorie</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Graphes aléatoires</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Random graphs</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zufallsgraph</subfield><subfield code="0">(DE-588)4277661-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Zufallsgraph</subfield><subfield code="0">(DE-588)4277661-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Cambridge series in statistical and probabilistic mathematics</subfield><subfield code="v">[20]</subfield><subfield code="w">(DE-604)BV011442366</subfield><subfield code="9">20</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/enhancements/fy0661/2006020925-d.html</subfield><subfield code="3">Publisher description</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/enhancements/fy0661/2006020925-t.html</subfield><subfield code="3">Table of contents only</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HEBIS Datenaustausch Darmstadt</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=014909048&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-014909048</subfield></datafield></record></collection> |
| id | DE-604.BV021695031 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:15:33Z |
| indexdate | 2024-07-09T20:41:51Z |
| institution | BVB |
| isbn | 9780521866569 0521866561 |
| language | English |
| lccn | 2006020925 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014909048 |
| oclc_num | 70219882 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-29T DE-83 DE-19 DE-BY-UBM |
| owner_facet | DE-91G DE-BY-TUM DE-29T DE-83 DE-19 DE-BY-UBM |
| physical | IX, 212 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge series in statistical and probabilistic mathematics |
| series2 | Cambridge series in statistical and probabilistic mathematics |
| spelling | Durrett, Richard 1951- Verfasser (DE-588)121396789 aut Random graph dynamics Rick Durrett 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 IX, 212 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge series in statistical and probabilistic mathematics [20] Includes bibliographical references Dynamica gtt Grafentheorie gtt Graphes aléatoires Random graphs Zufallsgraph (DE-588)4277661-2 gnd rswk-swf Zufallsgraph (DE-588)4277661-2 s DE-604 Cambridge series in statistical and probabilistic mathematics [20] (DE-604)BV011442366 20 http://www.loc.gov/catdir/enhancements/fy0661/2006020925-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0661/2006020925-t.html Table of contents only HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014909048&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Durrett, Richard 1951- Random graph dynamics Cambridge series in statistical and probabilistic mathematics Dynamica gtt Grafentheorie gtt Graphes aléatoires Random graphs Zufallsgraph (DE-588)4277661-2 gnd |
| subject_GND | (DE-588)4277661-2 |
| title | Random graph dynamics |
| title_auth | Random graph dynamics |
| title_exact_search | Random graph dynamics |
| title_exact_search_txtP | Random graph dynamics |
| title_full | Random graph dynamics Rick Durrett |
| title_fullStr | Random graph dynamics Rick Durrett |
| title_full_unstemmed | Random graph dynamics Rick Durrett |
| title_short | Random graph dynamics |
| title_sort | random graph dynamics |
| topic | Dynamica gtt Grafentheorie gtt Graphes aléatoires Random graphs Zufallsgraph (DE-588)4277661-2 gnd |
| topic_facet | Dynamica Grafentheorie Graphes aléatoires Random graphs Zufallsgraph |
| url | http://www.loc.gov/catdir/enhancements/fy0661/2006020925-d.html http://www.loc.gov/catdir/enhancements/fy0661/2006020925-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014909048&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011442366 |
| work_keys_str_mv | AT durrettrichard randomgraphdynamics |