Coverart for item
The Resource Bessel Processes, Schramm-Loewner Evolution, and the Dyson Model, by Makoto Katori, (electronic resource)

Bessel Processes, Schramm-Loewner Evolution, and the Dyson Model, by Makoto Katori, (electronic resource)

Label
Bessel Processes, Schramm-Loewner Evolution, and the Dyson Model
Title
Bessel Processes, Schramm-Loewner Evolution, and the Dyson Model
Statement of responsibility
by Makoto Katori
Creator
Subject
Language
eng
Summary
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 Ý is introduced as a multivariate extension of BES(D) with the relation D = Ý + 1. The book concentrates on the case where Ý = 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
Member of
http://library.link/vocab/creatorDate
1931-
http://library.link/vocab/creatorName
Katori, Makoto
Image bit depth
0
Literary form
non fiction
Series statement
SpringerBriefs in Mathematical Physics,
Series volume
11
http://library.link/vocab/subjectName
  • Mathematics
  • Probabilities
  • Mathematical physics
  • Statistical physics
  • Dynamical systems
Label
Bessel Processes, Schramm-Loewner Evolution, and the Dyson Model, by Makoto Katori, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-981-10-0275-5
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Preface -- 1 Bessel Process -- 2 Schramm-Loewner Evolution (SLE) -- 3 Dyson Model -- References -- Solutions -- Index
Control code
978-981-10-0275-5
Dimensions
unknown
Edition
1st ed. 2016.
Extent
1 online resource (x, 141 pages)
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9789811002755
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-981-10-0275-5
Other physical details
16 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)938557567
Label
Bessel Processes, Schramm-Loewner Evolution, and the Dyson Model, by Makoto Katori, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-981-10-0275-5
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Preface -- 1 Bessel Process -- 2 Schramm-Loewner Evolution (SLE) -- 3 Dyson Model -- References -- Solutions -- Index
Control code
978-981-10-0275-5
Dimensions
unknown
Edition
1st ed. 2016.
Extent
1 online resource (x, 141 pages)
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9789811002755
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-981-10-0275-5
Other physical details
16 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)938557567

Library Locations

    • Badia FiesolanaBorrow it
      Via dei Roccettini 9, San Domenico di Fiesole, 50014, IT
      43.803074 11.283055
Processing Feedback ...