Multi-time distribution in discrete polynuclear growth
Probability
2021-12-14 v3 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
We study the multi-time distribution in a discrete polynuclear growth model or, equivalently, in directed last-passage percolation with geometric weights. A formula for the joint multi-time distribution function is derived in the discrete setting. It takes the form of a multiple contour integral of a block Fredholm determinant. The asymptotic multi-time distribution is then computed by taking the appropriate KPZ-scaling limit of this formula. This distribution is expected to be universal for models in the Kardar-Parisi-Zhang universality class.
Cite
@article{arxiv.1906.01053,
title = {Multi-time distribution in discrete polynuclear growth},
author = {Kurt Johansson and Mustazee Rahman},
journal= {arXiv preprint arXiv:1906.01053},
year = {2021}
}
Comments
final version with minor corrections and additional references