Polynuclear growth model, GOE$^2$ and random matrix with deterministic source

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dc.creatorImamura, T.
dc.creatorSasamoto, T.
dc.date2004-11-17
dc.date.accessioned2026-07-07T04:31:38Z
dc.date.available2026-07-07T04:31:38Z
dc.descriptionWe present a random matrix interpretation of the distribution functions which have appeared in the study of the one-dimensional polynuclear growth (PNG) model with external sources. It is shown that the distribution, GOE$^2$, which is defined as the square of the GOE Tracy-Widom distribution, can be obtained as the scaled largest eigenvalue distribution of a special case of a random matrix model with a deterministic source, which have been studied in a different context previously. Compared to the original interpretation of the GOE$^2$ as ``the square of GOE'', ours has an advantage that it can also describe the transition from the GUE Tracy-Widom distribution to the GOE$^2$. We further demonstrate that our random matrix interpretation can be obtained naturally by noting the similarity of the topology between a certain non-colliding Brownian motion model and the multi-layer PNG model with an external source. This provides us with a multi-matrix model interpretation of the multi-point height distributions of the PNG model with an external source.
dc.description27pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math-ph/0411057
dc.identifierhttp://arxiv.org/abs/math-ph/0411057
dc.identifierPhys. Rev. E 71, 041606 (2005)
dc.identifierdoi:10.1103/PhysRevE.71.041606
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57890
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectProbability
dc.subjectExactly Solvable and Integrable Systems
dc.titlePolynuclear growth model, GOE$^2$ and random matrix with deterministic source
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