國立虎尾科技大學 |

Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model/ by Makoto Katori.
Author:	Katori, Makoto.
Description:	X, 141 p. 16 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematical physics. -
Online resource:	https://doi.org/10.1007/978-981-10-0275-5
ISBN:	9789811002755

Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model
Katori, Makoto.

Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model[electronic resource] /by Makoto Katori. - 1st ed. 2016. - X, 141 p. 16 illus. in color.online resource. - SpringerBriefs in Mathematical Physics,112197-1757 ;. - SpringerBriefs in Mathematical Physics,8.

Preface -- 1 Bessel Process -- 2 Schramm-Loewner Evolution (SLE) -- 3 Dyson Model -- References -- Solutions -- Index.

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. .

ISBN: 9789811002755

Standard No.: 10.1007/978-981-10-0275-5doiSubjects--Topical Terms:

527831
Mathematical physics.

LC Class. No.: QA401-425

Dewey Class. No.: 530.15

Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model
LDR:03060nam a22004095i 4500 001 981532
003 DE-He213
005 20200704083833.0
007 cr nn 008mamaa
008 201211s2016 si | s |||| 0|eng d
020 $a 9789811002755 $9 978-981-10-0275-5
024 7 $a 10.1007/978-981-10-0275-5 $2 doi
035 $a 978-981-10-0275-5
050 4 $a QA401-425
050 4 $a QC19.2-20.85
072 7 $a PHU $2 bicssc
072 7 $a SCI040000 $2 bisacsh
072 7 $a PHU $2 thema
082 0 4 $a 530.15 $2 23
100 1 $a Katori, Makoto. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1106177
245 1 0 $a Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model $h [electronic resource] / $c by Makoto Katori.
250 $a 1st ed. 2016.
264 1 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2016.
300 $a X, 141 p. 16 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a SpringerBriefs in Mathematical Physics, $x 2197-1757 ; $v 11
505 0 $a Preface -- 1 Bessel Process -- 2 Schramm-Loewner Evolution (SLE) -- 3 Dyson Model -- References -- Solutions -- Index.
520 $a 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. .
650 0 $a Mathematical physics. $3 527831
650 0 $a Probabilities. $3 527847
650 0 $a Statistical physics. $3 528048
650 0 $a Dynamical systems. $3 1249739
650 1 4 $a Mathematical Physics. $3 786661
650 2 4 $a Probability Theory and Stochastic Processes. $3 593945
650 2 4 $a Complex Systems. $3 888664
650 2 4 $a Statistical Physics and Dynamical Systems. $3 1114011
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9789811002748
776 0 8 $i Printed edition: $z 9789811002762
830 0 $a SpringerBriefs in Mathematical Physics, $x 2197-1757 ; $v 8 $3 1263793
856 4 0 $u https://doi.org/10.1007/978-981-10-0275-5
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)