A GUE central limit theorem and universality of directed first andlast passage site percolation
By Jinho Baik, T. Suidan. 2004
52 citations recorded by the source corpus.
We prove a GUE central limit theorem for random variables with finite fourth moment. We apply this theorem to prove that the directed first and last passage percolation problems in thin rectangles exhibit universal fluctuations given by the Tracy-Widom law.
Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/763e1546c1cd95c13ed447c06e27be9e98bde703
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In Artificial Intelligence
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Sparse regular random graphs: Spectral density and eigenvectors (2009, background): “Deift and Goiev [21] looked at different potential functions on symmetric, hermitian, and self-dual matrices; Baik and Suidan explored connections to percolation [8] and random walks [9]; β-generalizations of the classical ensembles and universal properties thereof have been explored in Forrester an”
- A Universality Property for Last-Passage Percolation Paths Close to the Axis (2004, unknown): “It seems unlikely that the value 3 / 7 in Theorem 1 represents a real threshold.”
- A generalization of the Lindeberg principle (2005, unknown): “It was recently observed by Toufic Suidan [18] that the results in [5] can be used to give an immediate proof of the universality of last passage percolation in thin rectangles (originally a result of [3] and [4]).”