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

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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Katori, Makoto (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Singapore : Springer Singapore : Imprint: Springer, 2016.
Έκδοση:1st ed. 2016.
Σειρά:SpringerBriefs in Mathematical Physics, 11
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
LEADER 03450nam a22005175i 4500
001 978-981-10-0275-5
003 DE-He213
005 20160210021142.0
007 cr nn 008mamaa
008 160208s2016 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 
040 |d GrThAP 
050 4 |a QA401-425 
050 4 |a QC19.2-20.85 
072 7 |a PHU  |2 bicssc 
072 7 |a SCI040000  |2 bisacsh 
082 0 4 |a 530.15  |2 23 
100 1 |a Katori, Makoto.  |e author. 
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 Mathematics. 
650 0 |a Probabilities. 
650 0 |a Mathematical physics. 
650 0 |a Statistical physics. 
650 0 |a Dynamical systems. 
650 1 4 |a Mathematics. 
650 2 4 |a Mathematical Physics. 
650 2 4 |a Probability Theory and Stochastic Processes. 
650 2 4 |a Statistical Physics, Dynamical Systems and Complexity. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9789811002748 
830 0 |a SpringerBriefs in Mathematical Physics,  |x 2197-1757 ;  |v 11 
856 4 0 |u http://dx.doi.org/10.1007/978-981-10-0275-5  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
950 |a Mathematics and Statistics (Springer-11649)