Airy Processes and Variational Problems

2013/01/31 by Jeremy Quastel, Daniel Remenik · 2 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Applied mathematics #Computer science #Mathematical economics #Mathematics #Random Matrices and Applications #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR

paper · pdf · doi:10.1007/978-1-4939-0339-9_5

Minor corrections. 41 pages, 4 figures. To appear as chapter in "PASI Proceedings: Topics in percolative and disordered systems"

arxiv created 2013/09/08 · crossref issued 2014/01/01 · crossref published 2014/01/01 · crossref published-print 2014/01/01 · openalex publication_date 2014/01/01 · crossref published-online 2014/06/17 · crossref created 2014/06/19 · arxiv updated 2020/10/15 · crossref deposited 2024/05/27 · openalex created_date 2025/10/10 · crossref indexed 2026/03/19 · openalex updated_date 2026/08/05

Abstract

We review the Airy processes; their formulation and how they are conjectured to govern the large time, large distance spatial fluctuations of one dimensional random growth models. We also describe formulas which express the probabilities that they lie below a given curve as Fredholm determinants of certain boundary value operators, and the several applications of these formulas to variational problems involving Airy processes that arise in physical problems, as well as to their local behaviour.

Citations

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Cited by

• Non-intersecting Brownian bridges and the Laguerre Orthogonal Ensemble
• Airy function [wikipedia]