Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues

Simple item page
dc.creatorFerrari, Patrik L.
dc.date2004-02-19
dc.date2004-06-17
dc.date.accessioned2026-07-07T04:30:58Z
dc.date.available2026-07-07T04:30:58Z
dc.descriptionWe consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. Through the Robinson-Schensted-Knuth (RSK) construction, one obtains the multilayer PNG model, which consists of a stack of non-intersecting lines, the top one being the PNG height. The statistics of the lines is translation invariant and at a fixed position the lines define a point process. We prove that for large times the edge of this point process, suitably scaled, has a limit. This limit is a Pfaffian point process and identical to the one obtained from the edge scaling of Gaussian orthogonal ensemble (GOE) of random matrices. Our results give further insight to the universality structure within the KPZ class of 1+1 dimensional growth models.
dc.description40 pages, 6 figures, LaTeX; Section 4 is substantially modified
dc.identifierhttps://arxiv.org/abs/math-ph/0402053
dc.identifierhttp://arxiv.org/abs/math-ph/0402053
dc.identifierComm. Math. Phys., 252 (2004), 77-109
dc.identifierdoi:10.1007/s00220-004-1204-6
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57656
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectProbability
dc.titlePolynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
dc.typetext

Files

Collections

arXiv