A random tiling model for two-dimensional electrostatics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2005
|
| Series: | Memoirs of the American Mathematical Society
839 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 178, number 839 (third of 5 numbers)." Includes bibliographical references |
| Physical Description: | IX, 144 S. graph. Darst. |
| ISBN: | 082183794X |
Staff View
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| 245 | 1 | 0 | |a A random tiling model for two-dimensional electrostatics |c Mihai Ciucu |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2005 | |
| 300 | |a IX, 144 S. |b graph. Darst. | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 839 | |
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| 500 | |a Includes bibliographical references | ||
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| 650 | 4 | |a Pavage (Mathématiques) | |
| 650 | 7 | |a Statistische mechanica |2 gtt | |
| 650 | 4 | |a Électrostatique | |
| 650 | 4 | |a Tiling (Mathematics) | |
| 650 | 4 | |a Electrostatics | |
| 650 | 4 | |a Statistical mechanics | |
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Record in the Search Index
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| adam_text | Contents
Abstract ix
Part A.
A Random Tiling Model for Two Dimensional Electrostatics 1
1. Introduction 3
2. Definitions, statement of results and physical interpretation 6
3. Reduction to boundary influenced correlations 16
4. A simple product formula for correlations along the boundary 18
5. A (2m + 2n) fold sum for w 25
6. Separation of the (2m+2n) fold sum for W in terms of 4mn fold integrals 37
7. The asymptotics of the T^ s and T (n) s 42
8. Replacement of the T^ s and T (fe) s by their asymptotics 52
9. Proof of Proposition 7.2 56
10. The asymptotics of a multidimensional Laplace integral 65
11. The asymptotics of wb. Proof of Theorem 2.2 69
12. Another simple product formula for correlations along the boundary 80
13. The asymptotics of wj. Proof of Theorem 2.1 84
14. A conjectured general two dimensional Superposition Principle 94
15. Three dimensions and concluding remarks 99
Bibliography 104
Part B.
Plane Partitions I: A Generalization of MacMahon s Formula 107
1. Introduction 109
2. Two families of regions 116
vii
viii CONTENTS
3. Reduction to simply connected regions 120
4. Recurrences for M(R tq(x)) and M(.Rliq(a;)) 125
5. Proof of Proposition 2.1 135
6. The guessing of M(R1m(x)) and M(Rhq(x)) 142
Bibliography 144
|
| adam_txt |
Contents
Abstract ix
Part A.
A Random Tiling Model for Two Dimensional Electrostatics 1
1. Introduction 3
2. Definitions, statement of results and physical interpretation 6
3. Reduction to boundary influenced correlations 16
4. A simple product formula for correlations along the boundary 18
5. A (2m + 2n) fold sum for w 25
6. Separation of the (2m+2n) fold sum for W in terms of 4mn fold integrals 37
7. The asymptotics of the T^'s and T'(n) 's 42
8. Replacement of the T^'s and T'(fe)'s by their asymptotics 52
9. Proof of Proposition 7.2 56
10. The asymptotics of a multidimensional Laplace integral 65
11. The asymptotics of wb. Proof of Theorem 2.2 69
12. Another simple product formula for correlations along the boundary 80
13. The asymptotics of wj. Proof of Theorem 2.1 84
14. A conjectured general two dimensional Superposition Principle 94
15. Three dimensions and concluding remarks 99
Bibliography 104
Part B.
Plane Partitions I: A Generalization of MacMahon's Formula 107
1. Introduction 109
2. Two families of regions 116
vii
viii CONTENTS
3. Reduction to simply connected regions 120
4. Recurrences for M(R\tq(x)) and M(.Rliq(a;)) 125
5. Proof of Proposition 2.1 135
6. The guessing of M(R1m(x)) and M(Rhq(x)) 142
Bibliography 144 |
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| dewey-full | 510 537/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 537 - Electricity and electronics |
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| dewey-search | 510 537/.2 |
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| dewey-tens | 510 - Mathematics 530 - Physics |
| discipline | Physik Mathematik |
| discipline_str_mv | Physik Mathematik |
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| index_date | 2024-07-02T13:28:43Z |
| indexdate | 2024-07-09T20:28:22Z |
| institution | BVB |
| isbn | 082183794X |
| language | English |
| lccn | 2005050800 |
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| physical | IX, 144 S. graph. Darst. |
| publishDate | 2005 |
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| series2 | Memoirs of the American Mathematical Society |
| spelling | Ciucu, Mihai 1968- Verfasser (DE-588)138737010 aut A random tiling model for two-dimensional electrostatics Mihai Ciucu Providence, RI American Mathematical Society 2005 IX, 144 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 839 "Volume 178, number 839 (third of 5 numbers)." Includes bibliographical references Combinatieleer gtt Elektrostatica gtt Mecânica estatística larpcal Mécanique statistique Pavage (Mathématiques) Statistische mechanica gtt Électrostatique Tiling (Mathematics) Electrostatics Statistical mechanics Elektrostatik (DE-588)4151975-9 gnd rswk-swf Überdeckung Mathematik (DE-588)4186551-0 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Überdeckung Mathematik (DE-588)4186551-0 s Elektrostatik (DE-588)4151975-9 s Statistische Mechanik (DE-588)4056999-8 s b DE-604 Memoirs of the American Mathematical Society 839 (DE-604)BV008000141 839 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014275097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ciucu, Mihai 1968- A random tiling model for two-dimensional electrostatics Memoirs of the American Mathematical Society Combinatieleer gtt Elektrostatica gtt Mecânica estatística larpcal Mécanique statistique Pavage (Mathématiques) Statistische mechanica gtt Électrostatique Tiling (Mathematics) Electrostatics Statistical mechanics Elektrostatik (DE-588)4151975-9 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd Statistische Mechanik (DE-588)4056999-8 gnd |
| subject_GND | (DE-588)4151975-9 (DE-588)4186551-0 (DE-588)4056999-8 |
| title | A random tiling model for two-dimensional electrostatics |
| title_auth | A random tiling model for two-dimensional electrostatics |
| title_exact_search | A random tiling model for two-dimensional electrostatics |
| title_exact_search_txtP | A random tiling model for two-dimensional electrostatics |
| title_full | A random tiling model for two-dimensional electrostatics Mihai Ciucu |
| title_fullStr | A random tiling model for two-dimensional electrostatics Mihai Ciucu |
| title_full_unstemmed | A random tiling model for two-dimensional electrostatics Mihai Ciucu |
| title_short | A random tiling model for two-dimensional electrostatics |
| title_sort | a random tiling model for two dimensional electrostatics |
| topic | Combinatieleer gtt Elektrostatica gtt Mecânica estatística larpcal Mécanique statistique Pavage (Mathématiques) Statistische mechanica gtt Électrostatique Tiling (Mathematics) Electrostatics Statistical mechanics Elektrostatik (DE-588)4151975-9 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd Statistische Mechanik (DE-588)4056999-8 gnd |
| topic_facet | Combinatieleer Elektrostatica Mecânica estatística Mécanique statistique Pavage (Mathématiques) Statistische mechanica Électrostatique Tiling (Mathematics) Electrostatics Statistical mechanics Elektrostatik Überdeckung Mathematik Statistische Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014275097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT ciucumihai arandomtilingmodelfortwodimensionalelectrostatics |