Fluctuations of the onedimensional polynuclear growth model with external sources
Abstract
The onedimensional polynuclear growth model with external sources at edges is studied. The height fluctuation at the origin is known to be given by either the Gaussian, the GUE TracyWidom distribution, or certain distributions called GOE ^{2} and F, depending on the strength of the sources. We generalize these results and show that the scaling limit of the multipoint equal time height fluctuations of the model are described by the Fredholm determinant, of which the limiting kernel is explicitly obtained. In particular, we obtain two new kernels, describing transitions between the above onepoint distributions. One expresses the transition from the GOE ^{2} to the GUE TracyWidom distribution or to the Gaussian; the other the transition from F to the Gaussian. The results specialized to the fluctuation at the origin are shown to be equivalent to the previously obtained ones via the RiemannHilbert method.
 Publication:

Nuclear Physics B
 Pub Date:
 November 2004
 DOI:
 10.1016/j.nuclphysb.2004.07.030
 arXiv:
 arXiv:mathph/0406001
 Bibcode:
 2004NuPhB.699..503I
 Keywords:

 Mathematical Physics;
 Condensed Matter  Statistical Mechanics;
 Mathematics  Mathematical Physics;
 Mathematics  Probability;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 43 pages, 4 figures