Percolation:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1999
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
321 |
| Schlagworte: | |
| Online-Zugang: | UBM01 Volltext |
| Beschreibung: | Percolation theory is the study of an idealized random medium in two or more dimensions. It is a cornerstone of the theory of spatial stochastic processes with applications in such fields as statistical physics, epidemiology, and the spread of populations. Percolation plays a pivotal role in studying more complex systems exhibiting phase transition. The mathematical theory is mature, but continues to give rise to problems of special beauty and difficulty. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. The book is intended for graduate students and researchers in probability and mathematical physics. Almost no specialist knowledge is assumed beyond undergraduate analysis and probability. This new volume differs substantially from the first edition through the inclusion of much new material, including: the rigorous theory of dynamic and static renormalization; a sketch of the lace expansion and mean field theory; the uniqueness of the infinite cluster; strict inequalities between critical probabilities; several essays on related fields and applications; numerous other results of significant. There is a summary of the hypotheses of conformal invariance. A principal feature of the process is the phase transition. The subcritical and supercritical phases are studied in detail. There is a guide for mathematicians to the physical theory of scaling and critical exponents, together with selected material describing the current state of the rigorous theory. To derive a rigorous theory of the phase transition remains an outstanding and beautiful problem of mathematics |
| Beschreibung: | 1 Online-Ressource (XIII, 447 p) |
| ISBN: | 9783662039816 9783642084423 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-662-03981-6 |
Internformat
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| 490 | 0 | |a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |v 321 |x 0072-7830 | |
| 500 | |a Percolation theory is the study of an idealized random medium in two or more dimensions. It is a cornerstone of the theory of spatial stochastic processes with applications in such fields as statistical physics, epidemiology, and the spread of populations. Percolation plays a pivotal role in studying more complex systems exhibiting phase transition. The mathematical theory is mature, but continues to give rise to problems of special beauty and difficulty. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. The book is intended for graduate students and researchers in probability and mathematical physics. Almost no specialist knowledge is assumed beyond undergraduate analysis and probability. This new volume differs substantially from the first edition through the inclusion of much new material, including: the rigorous theory of dynamic and static renormalization; a sketch of the lace expansion and mean field theory; the uniqueness of the infinite cluster; strict inequalities between critical probabilities; several essays on related fields and applications; numerous other results of significant. There is a summary of the hypotheses of conformal invariance. A principal feature of the process is the phase transition. The subcritical and supercritical phases are studied in detail. There is a guide for mathematicians to the physical theory of scaling and critical exponents, together with selected material describing the current state of the rigorous theory. To derive a rigorous theory of the phase transition remains an outstanding and beautiful problem of mathematics | ||
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Datensatz im Suchindex
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| author | Grimmett, Geoffrey 1950- |
| author_GND | (DE-588)120872919 |
| author_facet | Grimmett, Geoffrey 1950- |
| author_role | aut |
| author_sort | Grimmett, Geoffrey 1950- |
| author_variant | g g gg |
| building | Verbundindex |
| bvnumber | BV042423287 |
| classification_tum | MAT 000 |
| collection | ZDB-30-PQE ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863887039 (DE-599)BVBBV042423287 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-03981-6 |
| edition | Second Edition |
| format | Electronic eBook |
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| id | DE-604.BV042423287 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662039816 9783642084423 |
| issn | 0072-7830 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858704 |
| oclc_num | 863887039 |
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| physical | 1 Online-Ressource (XIII, 447 p) |
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| publishDate | 1999 |
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| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Grimmett, Geoffrey 1950- Verfasser (DE-588)120872919 aut Percolation by Geoffrey Grimmett Second Edition Berlin, Heidelberg Springer Berlin Heidelberg 1999 1 Online-Ressource (XIII, 447 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 321 0072-7830 Percolation theory is the study of an idealized random medium in two or more dimensions. It is a cornerstone of the theory of spatial stochastic processes with applications in such fields as statistical physics, epidemiology, and the spread of populations. Percolation plays a pivotal role in studying more complex systems exhibiting phase transition. The mathematical theory is mature, but continues to give rise to problems of special beauty and difficulty. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. The book is intended for graduate students and researchers in probability and mathematical physics. Almost no specialist knowledge is assumed beyond undergraduate analysis and probability. This new volume differs substantially from the first edition through the inclusion of much new material, including: the rigorous theory of dynamic and static renormalization; a sketch of the lace expansion and mean field theory; the uniqueness of the infinite cluster; strict inequalities between critical probabilities; several essays on related fields and applications; numerous other results of significant. There is a summary of the hypotheses of conformal invariance. A principal feature of the process is the phase transition. The subcritical and supercritical phases are studied in detail. There is a guide for mathematicians to the physical theory of scaling and critical exponents, together with selected material describing the current state of the rigorous theory. To derive a rigorous theory of the phase transition remains an outstanding and beautiful problem of mathematics Mathematics Combinatorics Distribution (Probability theory) Probability Theory and Stochastic Processes Theoretical, Mathematical and Computational Physics Mathematik Statistische Physik (DE-588)4057000-9 gnd rswk-swf Perkolationstheorie (DE-588)4323583-9 gnd rswk-swf Perkolation (DE-588)4115530-0 gnd rswk-swf Perkolation (DE-588)4115530-0 s Statistische Physik (DE-588)4057000-9 s 1\p DE-604 Perkolationstheorie (DE-588)4323583-9 s 2\p DE-604 https://doi.org/10.1007/978-3-662-03981-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Grimmett, Geoffrey 1950- Percolation Mathematics Combinatorics Distribution (Probability theory) Probability Theory and Stochastic Processes Theoretical, Mathematical and Computational Physics Mathematik Statistische Physik (DE-588)4057000-9 gnd Perkolationstheorie (DE-588)4323583-9 gnd Perkolation (DE-588)4115530-0 gnd |
| subject_GND | (DE-588)4057000-9 (DE-588)4323583-9 (DE-588)4115530-0 |
| title | Percolation |
| title_auth | Percolation |
| title_exact_search | Percolation |
| title_full | Percolation by Geoffrey Grimmett |
| title_fullStr | Percolation by Geoffrey Grimmett |
| title_full_unstemmed | Percolation by Geoffrey Grimmett |
| title_short | Percolation |
| title_sort | percolation |
| topic | Mathematics Combinatorics Distribution (Probability theory) Probability Theory and Stochastic Processes Theoretical, Mathematical and Computational Physics Mathematik Statistische Physik (DE-588)4057000-9 gnd Perkolationstheorie (DE-588)4323583-9 gnd Perkolation (DE-588)4115530-0 gnd |
| topic_facet | Mathematics Combinatorics Distribution (Probability theory) Probability Theory and Stochastic Processes Theoretical, Mathematical and Computational Physics Mathematik Statistische Physik Perkolationstheorie Perkolation |
| url | https://doi.org/10.1007/978-3-662-03981-6 |
| work_keys_str_mv | AT grimmettgeoffrey percolation |