Bessel Process, Schramm-Loewner Evolution, and the Dyson Model
(Sprache: Englisch)
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...
Voraussichtlich lieferbar in 3 Tag(en)
versandkostenfrei
Buch (Kartoniert)
Fr. 71.00
inkl. MwSt.
- Kreditkarte, Paypal, Rechnungskauf
- 30 Tage Widerrufsrecht
Produktdetails
Produktinformationen zu „Bessel Process, Schramm-Loewner Evolution, and the Dyson Model “
Klappentext zu „Bessel Process, 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 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 beta is introduced as a multivariate extension of BES(D) with the relation D = beta + 1. The book concentrates on the case where beta = 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.
Inhaltsverzeichnis zu „Bessel Process, Schramm-Loewner Evolution, and the Dyson Model “
Preface.- 1 Bessel Process.- 2 Schramm-Loewner Evolution (SLE).- 3 Dyson Model.- References.- Solutions.- Index.
Bibliographische Angaben
- Autor: Makoto Katori
- 2016, 1st ed. 2016, X, 141 Seiten, 141 farbige Abbildungen, Masse: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 9811002746
- ISBN-13: 9789811002748
- Erscheinungsdatum: 16.02.2016
Sprache:
Englisch
Kommentar zu "Bessel Process, Schramm-Loewner Evolution, and the Dyson Model"
0 Gebrauchte Artikel zu „Bessel Process, Schramm-Loewner Evolution, and the Dyson Model“
Zustand | Preis | Porto | Zahlung | Verkäufer | Rating |
---|
Schreiben Sie einen Kommentar zu "Bessel Process, Schramm-Loewner Evolution, and the Dyson Model".
Kommentar verfassen