Bessel processes, Schramm–Loewner evolution, and the Dyson model:
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore
Springer
[2016]
|
| Series: | SpringerBriefs in mathematical physics
volume 11 |
| Subjects: | |
| Online Access: | BTU01 FHR01 FRO01 TUM01 UBM01 UBT01 UBW01 UEI01 UPA01 Volltext Abstract Inhaltsverzeichnis |
| Physical Description: | 1 Online Ressource (X, 141 Seiten, 16 illus. in color) |
| ISBN: | 9789811002755 |
| ISSN: | 2197-1757 |
| DOI: | 10.1007/978-981-10-0275-5 |
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Record in the Search Index
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|---|---|
| adam_text | BESSEL PROCESSES, SCHRAMM–LOEWNER EVOLUTION, AND THE DYSON MODEL
/ KATORI, MAKOTO
: 2016
ABSTRACT / INHALTSTEXT
THE PURPOSE OF THIS BOOK IS TO INTRODUCE TWO RECENT TOPICS IN
MATHEMATICAL PHYSICS AND PROBABILITY THEORY: THE SCHRAMM–LOEWNER
EVOLUTION (SLE) AND INTERACTING PARTICLE SYSTEMS RELATED TO RANDOM
MATRIX THEORY. A TYPICAL EXAMPLE OF THE LATTER SYSTEMS IS DYSON S
BROWNIAN MOTION (BM) MODEL. THE SLE AND DYSON S BM MODEL MAY BE
CONSIDERED AS CHILDREN OF THE BESSEL PROCESS WITH PARAMETER D, BES(D),
AND THE SLE AND DYSON S BM MODEL AS GRANDCHILDREN OF BM. IN CHAP. 1
THE PARENTHOOD OF BM IN DIFFUSION PROCESSES IS CLARIFIED AND BES(D) IS
DEFINED FOR ANY D ≥ 1. DEPENDENCE OF THE BES(D) PATH ON ITS INITIAL
VALUE IS REPRESENTED BY THE BESSEL FLOW. IN CHAP. 2 SLE IS INTRODUCED AS
A COMPLEXIFICATION OF BES(D). RICH MATHEMATICS AND PHYSICS INVOLVED IN
SLE ARE DUE TO THE NONTRIVIAL DEPENDENCE OF THE BESSEL FLOW ON D. FROM A
RESULT FOR THE BESSEL FLOW, CARDY S FORMULA IN CARLESON S FORM IS
DERIVED FOR SLE. IN CHAP. 3 DYSON S BM MODEL WITH PARAMETER Β IS
INTRODUCED AS A MULTIVARIATE EXTENSION OF BES(D) WITH THE RELATION D =
Β + 1. THE BOOK CONCENTRATES ON THE CASE WHERE Β = 2 AND CALLS THIS
CASE SIMPLY THE DYSON MODEL. THE DYSON MODEL INHERITS THE TWO ASPECTS OF
BES(3); HENCE IT HAS VERY STRONG SOLVABILITY. THAT IS, THE PROCESS IS
PROVED TO BE DETERMINANTAL IN THE SENSE THAT ALL SPATIO-TEMPORAL
CORRELATION FUNCTIONS ARE GIVEN BY DETERMINANTS, AND ALL OF THEM ARE
CONTROLLED BY A SINGLE FUNCTION CALLED THE CORRELATION KERNEL. FROM THE
DETERMINANTAL STRUCTURE OF THE DYSON MODEL, THE TRACY–WIDOM
DISTRIBUTION IS DERIVED.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
BESSEL PROCESSES, SCHRAMM–LOEWNER EVOLUTION, AND THE DYSON MODEL
/ KATORI, MAKOTO
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PREFACE
1 BESSEL PROCESS
2 SCHRAMM-LOEWNER EVOLUTION (SLE)
3 DYSON MODEL
REFERENCES
SOLUTIONS
INDEX
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Katori, Makoto |
| author_facet | Katori, Makoto |
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| dewey-full | 530.15 |
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| dewey-ones | 530 - Physics |
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| dewey-search | 530.15 |
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| discipline | Physik Mathematik |
| doi_str_mv | 10.1007/978-981-10-0275-5 |
| format | Electronic eBook |
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| spelling | Katori, Makoto Verfasser aut Bessel processes, Schramm–Loewner evolution, and the Dyson model Makoto Katori Singapore Springer [2016] © 2016 1 Online Ressource (X, 141 Seiten, 16 illus. in color) txt rdacontent c rdamedia cr rdacarrier SpringerBriefs in mathematical physics volume 11 2197-1757 Mathematics Probabilities Mathematical physics Statistical physics Dynamical systems Mathematical Physics Probability Theory and Stochastic Processes Statistical Physics, Dynamical Systems and Complexity Mathematik Mathematische Physik Erscheint auch als Druckausgabe 978-981-10-0274-8 SpringerBriefs in mathematical physics volume 11 (DE-604)BV041997379 11 https://doi.org/10.1007/978-981-10-0275-5 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028840818&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Abstract Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028840818&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Katori, Makoto Bessel processes, Schramm–Loewner evolution, and the Dyson model SpringerBriefs in mathematical physics Mathematics Probabilities Mathematical physics Statistical physics Dynamical systems Mathematical Physics Probability Theory and Stochastic Processes Statistical Physics, Dynamical Systems and Complexity Mathematik Mathematische Physik |
| title | Bessel processes, Schramm–Loewner evolution, and the Dyson model |
| title_auth | Bessel processes, Schramm–Loewner evolution, and the Dyson model |
| title_exact_search | Bessel processes, Schramm–Loewner evolution, and the Dyson model |
| title_full | Bessel processes, Schramm–Loewner evolution, and the Dyson model Makoto Katori |
| title_fullStr | Bessel processes, Schramm–Loewner evolution, and the Dyson model Makoto Katori |
| title_full_unstemmed | Bessel processes, Schramm–Loewner evolution, and the Dyson model Makoto Katori |
| title_short | Bessel processes, Schramm–Loewner evolution, and the Dyson model |
| title_sort | bessel processes schramm loewner evolution and the dyson model |
| topic | Mathematics Probabilities Mathematical physics Statistical physics Dynamical systems Mathematical Physics Probability Theory and Stochastic Processes Statistical Physics, Dynamical Systems and Complexity Mathematik Mathematische Physik |
| topic_facet | Mathematics Probabilities Mathematical physics Statistical physics Dynamical systems Mathematical Physics Probability Theory and Stochastic Processes Statistical Physics, Dynamical Systems and Complexity Mathematik Mathematische Physik |
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