Discrete Polynuclear Growth and Determinantal Processes

2002/06/30 by Kurt Johansson · 448 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Mathematics #Random Matrices and Applications #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR

paper · pdf · doi:10.1007/s00220-003-0945-y

published in Communications in Mathematical Physics 242(1-2), 277-329 (Springer Science+Business Media) · In the new version some parts have been replaced, new material has beeb added and errors corrected

arxiv created 2002/11/26 · openalex publication_date 2003/10/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider a discrete polynuclear growth (PNG) process and prove a functioal limit theorem for its convergrence to the Airy process. This generalizes previous results by Pr"ahofer and Spohn. The result enables us to express the GOE largest eigenvalue (Tracy-Widom) distribution in terms of the Airy process. We also show some results and give a conjecture about the transversal fluctuations in a point to line last passage percolation problem.

Citations

• Correlation Functions, Cluster Functions, and Spacing Distributions for Random Matrices
• On the distribution of the length of the longest increasing subsequence of random permutations
• Universality of the Local Spacing Distribution¶in Certain Ensembles of Hermitian Wigner Matrices
• Matrices coupled in a chain. I. Eigenvalue correlations
• A Brownian-Motion Model for the Eigenvalues of a Random Matrix
• Infinite wedge and random partitions
• Local statistics of lattice dimers
• Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges
• Determinantal random point fields
• Optimal tail estimates for directed last passage site percolation with geometric random variables

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