Disorder and critical phenomena through basic probability models: École d'Été de Probabilités de Saint-Flour XL - 2010
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Schriftenreihe: | Lecture notes in mathematics
2025 : École d'Été de Probabilités de Saint-Flour |
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=3713544&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024380353&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 130 S. Ill., graph. Darst. |
| ISBN: | 3642211550 9783642211553 |
Internformat
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| 100 | 1 | |a Giacomin, Giambattista |e Verfasser |0 (DE-588)1014937876 |4 aut | |
| 245 | 1 | 0 | |a Disorder and critical phenomena through basic probability models |b École d'Été de Probabilités de Saint-Flour XL - 2010 |c Giambattista Giacomin |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2011 | |
| 300 | |a XI, 130 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 2025 : École d'Été de Probabilités de Saint-Flour | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 B 999-2025 |
|---|---|
| DE-BY-TUM_katkey | 1782350 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010214109 |
| _version_ | 1821934954012999680 |
| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION 1
REFERENCES 4
2 HOMOGENEOUS PINNING SYSTEMS: A CLASS OF EXACTLY SOLVED MODELS 5
2.1 WHAT HAPPENS IF WE REWARD A RANDOM WALK WHEN IT TOUCHES THE ORIGIN?
5
2.1.1 THE RANDOM WALK PINNING MODEL 5
2.1.2 VISITS TO THE ORIGIN AND THE COMPUTATION OF THE PARTITION FUNCTION
7
2.1.3 FROM PARTITION FUNCTION ESTIMATES TO PROPERTIES OF THE SYSTEM 10
2.2 THE GENERAL HOMOGENEOUS PINNING MODEL 14
2.3 PHASE TRANSITION AND CRITICAL BEHAVIOR 18
2.4 A FIRST LOOK AT A CRUCIAL NOTION: THE CORRELATION LENGTH 19 2.5 WHY
DO PEOPLE LOOK AT PINNING MODELS? A MODELING INTERMEZZO 21
2.5.1 POLYMER PINNING BY A DEFECT 21
2.5.2 INTERFACES IN TWO DIMENSIONS 21
2.5.3 DNA DENATURATION: THE POLAND-SCHERAGA MODEL 24 2.6 A LOOK AT THE
LITERATURE 24
REFERENCES 26
3 INTRODUCTION TO DISORDERED PINNING MODELS 29
3.1 THE DISORDERED PINNING MODEL 29
3.2 SUPER-ADDITIVITY, FREE ENERGY, AND LOCALIZATION 32
3.2.1 TWO IMPORTANT REMARKS 34
3.3 SELF-AVERAGING PROPERTY, EFFECT OF BOUNDARY CONDITION 35 3.3.1 PROOF
OF PROPOSITION 3.2 35
3.3.2 FREE AND CONSTRAINED MODELS 37
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1011288478
DIGITALISIERT DURCH
IMAGE 2
VIII CONTENTS
3.4 A LOOK AT THE LITERATURE AND, ONCE AGAIN, CORRELATION LENGTH ISSUES
38
REFERENCES 40
4 IRRELEVANT DISORDER ESTIMATES 41
4.1 DISORDER AND CRITICAL BEHAVIOR: WHAT TO EXPECT? 41
4.1.1 FIRST APPROACH: AN EXPANSION IN POWERS OF SS 2 42
4.1.2 SECOND APPROACH: A 2-REPLICA ARGUMENT 44
4.2 DISORDER IS IRRELEVANT IF A 1/2 (AND IF SS IS NOT TOO LARGE): A
PROOF 46
4.3 A LOOK AT THE LITERATURE 49
REFERENCES 50
5 RELEVANT DISORDER ESTIMATES: THE SMOOTHING PHENOMENON 51 5.1 SMOOTHING
FOR GAUSSIAN CHARGES: THE RARE STRETCH STRATEGY 51 5.2 MORE GENERAL
CHARGE DISTRIBUTIONS 55
5.3 BACK TO AND BEYOND HARRIS CRITERION: DISORDER AND SMOOTHING 55 5.3.1
DISORDER AND PHASE TRANSITIONS 56
5.3.2 HARRIS HEURISTIC ARGUMENT 57
5.3.3 RELEVANCE AND IRRELEVANCE 58
5.3.4 THE DILUTED ISING MODEL 58
5.3.5 RANDOM EXTERNAL FIELDS 59
5.4 A FURTHER LOOK AT THE LITERATURE 60
REFERENCES 60
6 CRITICAL POINT SHIFT: THE FRACTIONAL MOMENT METHOD 63 6.1 MAIN RESULT
AND OVERVIEW 63
6.2 THE BASIC FRACTIONAL MOMENT ESTIMATES 65
6.3 T H E A 1 CASE 67
6.3.1 A DIFFERENT LOOK ON PROPOSITION 6.3 67
6.3.2 A FIRST COARSE GRAINING PROCEDURE: ITERATED FRACTIONAL MOMENT
ESTIMATES 68
6.3.3 FINITE VOLUME ESTIMATES: THE PROOF OF THEOREM 6.1 FOR A 1 70
6.4 T H E A = L C A SE 74
6.5 THE A 6 (1/2,1) CASE 75
6.5.1 BOUNDS FOR CORRELATION LENGTH SIZE SYSTEMS 76 6.5.2 PROOF OF
THEOREM 6.1, CASE A *(1/2,1) 78
6.6 T H E A= L/2CASE 79
6.6.1 ESTIMATES UP TO THE (ANNEALED) CORRELATION LENGTH: GAUSSIAN CASE
79
6.6.2 BEYOND THE CORRELATION LENGTH: THEPROOFOFTHEOREM6.1(A=L/2) 83
6.7 A LOOK AT THE LITERATURE 87
REFERENCES 88
IMAGE 3
CONTENTS IX
7 THE COARSE GRAINING PROCEDURE 91
7.1 COARSE GRAINING ESTIMATES 91
REFERENCES 99
8 PATH PROPERTIES 101
8.1 OVERVIEW 101
8.2 A QUICK LOOK AT CONCENTRATION INEQUALITIES 102
8.3 THE LOCALIZED REGIME 104
8.3.1 A BASIC OBSERVATION (AND ITS CONSEQUENCES) 104 8.3.2
ON/I(/3,A)ANDF(/J,A) 106
8.4 THE DELOCALIZED REGIME 108
8.5 PATH BEHAVIOR: OVERVIEW OF WHAT IS KNOWN AND WHAT IS NOT 109 8.5.1
ON THE LOCALIZED (AND CRITICAL) REGIME 110
8.5.2 ON THE DELOCALIZED REGIME I LL
REFERENCES I LL
A DISCRETE RENEWAL THEORY: BASIC (AND A FEW LESS BASIC) FACTS AND
ESTIMATES 113
A.I A CRASH COURSE ON RENEWAL THEORY 113
A. 1.1 RENEWAL AND MARKOV CHAINS 113
A.1.2 THE RENEWAL THEOREM 114
A.1.3 BEYOND THE RENEWAL THEOREM 115
A. 1.4 CONVERGENCE OF RENEWAL AND POINT PROCESSES 116 A.2 SOME PINNING
ORIENTED RENEWAL ISSUES 117
A.2.1 ON BOUNDARY EFFECTS 117
A.2.2 TWO SCALING RESULTS FOR RENEWAL PROCESSES 118 A.2.3 ON THE
DERIVATIVES OF THE FREE ENERGY NEAR CRITICALITY 122 REFERENCES 125
INDEX 127
LIST OF PARTICIPANTS 129
|
| any_adam_object | 1 |
| author | Giacomin, Giambattista |
| author_GND | (DE-588)1014937876 |
| author_facet | Giacomin, Giambattista |
| author_role | aut |
| author_sort | Giacomin, Giambattista |
| author_variant | g g gg |
| building | Verbundindex |
| bvnumber | BV039528021 |
| classification_rvk | SI 850 |
| classification_tum | PHY 057f MAT 609f PHY 065f |
| ctrlnum | (OCoLC)748698799 (DE-599)DNB1011288478 |
| dewey-full | 530.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13 |
| dewey-search | 530.13 |
| dewey-sort | 3530.13 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV039528021 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T15:56:37Z |
| institution | BVB |
| isbn | 3642211550 9783642211553 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024380353 |
| oclc_num | 748698799 |
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| owner | DE-188 DE-83 DE-11 DE-824 DE-91G DE-BY-TUM |
| owner_facet | DE-188 DE-83 DE-11 DE-824 DE-91G DE-BY-TUM |
| physical | XI, 130 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spellingShingle | Giacomin, Giambattista Disorder and critical phenomena through basic probability models École d'Été de Probabilités de Saint-Flour XL - 2010 Lecture notes in mathematics Stochastisches Modell (DE-588)4057633-4 gnd Kritisches Phänomen (DE-588)4165788-3 gnd Phasenumwandlung (DE-588)4132140-6 gnd Ungeordnetes System (DE-588)4124353-5 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4165788-3 (DE-588)4132140-6 (DE-588)4124353-5 |
| title | Disorder and critical phenomena through basic probability models École d'Été de Probabilités de Saint-Flour XL - 2010 |
| title_auth | Disorder and critical phenomena through basic probability models École d'Été de Probabilités de Saint-Flour XL - 2010 |
| title_exact_search | Disorder and critical phenomena through basic probability models École d'Été de Probabilités de Saint-Flour XL - 2010 |
| title_full | Disorder and critical phenomena through basic probability models École d'Été de Probabilités de Saint-Flour XL - 2010 Giambattista Giacomin |
| title_fullStr | Disorder and critical phenomena through basic probability models École d'Été de Probabilités de Saint-Flour XL - 2010 Giambattista Giacomin |
| title_full_unstemmed | Disorder and critical phenomena through basic probability models École d'Été de Probabilités de Saint-Flour XL - 2010 Giambattista Giacomin |
| title_short | Disorder and critical phenomena through basic probability models |
| title_sort | disorder and critical phenomena through basic probability models ecole d ete de probabilites de saint flour xl 2010 |
| title_sub | École d'Été de Probabilités de Saint-Flour XL - 2010 |
| topic | Stochastisches Modell (DE-588)4057633-4 gnd Kritisches Phänomen (DE-588)4165788-3 gnd Phasenumwandlung (DE-588)4132140-6 gnd Ungeordnetes System (DE-588)4124353-5 gnd |
| topic_facet | Stochastisches Modell Kritisches Phänomen Phasenumwandlung Ungeordnetes System |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3713544&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024380353&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT giacomingiambattista disorderandcriticalphenomenathroughbasicprobabilitymodelsecoledetedeprobabilitesdesaintflourxl2010 |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 001z 2001 B 999-2025
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |