Universität zu Köln

Kriecherbauer, Thomas and Krug, Joachim ORCID: 0000-0002-2143-6490 (2010). A pedestrian's view on interacting particle systems, KPZ universality and random matrices. J. Phys. A-Math. Theor., 43 (40). BRISTOL: IOP PUBLISHING LTD. ISSN 1751-8121

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Abstract

These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 Symmetries and Universality in Mesoscopic Systems to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the basic physical concepts of equilibrium and nonequilibrium states, the one-dimensional simple exclusion process is introduced as a paradigmatic nonequilibrium interacting particle system. The stationary measure on the ring is derived and the idea of the hydrodynamic limit is sketched. We then introduce the phenomenological Kardar-Parisi-Zhang (KPZ) equation and explain the associated universality conjecture for surface fluctuations in growth models. This is followed by a detailed exposition of a seminal paper of Johansson [59] that relates the current fluctuations of the totally asymmetric simple exclusion process (TASEP) to the Tracy-Widom distribution of random matrix theory. The implications of this result are discussed within the framework of the KPZ conjecture.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kriecherbauer, Thomas UNSPECIFIED UNSPECIFIED UNSPECIFIED Krug, Joachim UNSPECIFIED orcid.org/0000-0002-2143-6490 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-494392
DOI:	10.1088/1751-8113/43/40/403001
Journal or Publication Title:	J. Phys. A-Math. Theor.
Volume:	43
Number:	40
Date:	2010
Publisher:	IOP PUBLISHING LTD
Place of Publication:	BRISTOL
ISSN:	1751-8121
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SIMPLE EXCLUSION PROCESS; POLYNUCLEAR GROWTH-MODEL; DIRECTED POLYMERS; ORTHOGONAL POLYNOMIALS; STATISTICAL-MECHANICS; SPACING DISTRIBUTIONS; LARGEST EIGENVALUE; STRONG ASYMPTOTICS; AIRY(2) PROCESSES; SCALE-INVARIANCE Multiple languages Physics, Multidisciplinary; Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/49439