One-dimensional stochastic growth and Gaussian ensembles of random matrices
Ferrari, Patrik L. ; Praehofer, Michael
arXiv, 0505038 / Harvested from arXiv
Text on arXiv
In this review paper we consider the polynuclear growth (PNG) model in one spatial dimension and its relation to random matrix ensembles. For curved and flat growth the scaling functions of the surface fluctuations coincide with limit distribution functions coming from certain Gaussian ensembles of random matrices. This connection can be explained via point processes associated to the PNG model and the random matrices ensemble by an extension to the multilayer PNG and multi-matrix models, respectively. We also explain other models which are equivalent to the PNG model: directed polymers, the longest increasing subsequence problem, Young tableaux, a directed percolation model, kink-antikink gas, and Hammersley process.
Publié le : 2005-05-13
Classification:  Mathematical Physics,  82C05,  15A52,  60G55 
@article{0505038,
     author = {Ferrari, Patrik L. and Praehofer, Michael},
     title = {One-dimensional stochastic growth and Gaussian ensembles of random
  matrices},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0505038}
}

Ferrari, Patrik L.; Praehofer, Michael. One-dimensional stochastic growth and Gaussian ensembles of random
  matrices. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0505038/