English

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.

Keywords

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

R2 v1 2026-06-23T09:39:57.333Z