Multi-time distribution in discrete polynuclear growth

Johansson, Kurt; Rahman, Mustazee

Abstract

We study the multitime distribution in a discrete polynuclear growth model or, equivalently, in directed last‐passage percolation with geometric weights. A formula for the joint multitime distribution function is derived in the discrete setting. It takes the form of a multiple contour integral of a block Fredholm determinant. The asymptotic multitime 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. © 2020 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.

Citation

Johansson, K., & Rahman, M. (2021). Multi-time distribution in discrete polynuclear growth. Communications on Pure and Applied Mathematics, 74(12), 2561-2627. https://doi.org/10.1002/cpa.21980

• Journal Article Type: Article
• Acceptance Date: Apr 3, 2020
• Online Publication Date: Feb 22, 2021
• Publication Date: 2021-12
• Deposit Date: Apr 18, 2020
• Publicly Available Date: Feb 22, 2022
• Journal: Communications on Pure and Applied Mathematics
• Print ISSN: 0010-3640
• Electronic ISSN: 1097-0312
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 74
• Issue: 12
• Pages: 2561-2627
• DOI: https://doi.org/10.1002/cpa.21980
• Public URL: https://durham-repository.worktribe.com/output/1273120
• Related Public URLs: https://arxiv.org/abs/1906.01053