A GUE Central Limit Theorem and Universality of Directed First and Last Passage Site Percolation

Details A GUE Central Limit Theorem and Universality of Directed First and Last Passage Site Percolation A GUE Central Limit Theorem and Universality of Directed First and Last Passage Site Percolation

2004-12-18

arxiv.org/abs/math/0412369v2

Mathematics

Probability

8 pages. To appear in IMRN

Scientific paper

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.

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