Transversal fluctuations for increasing subsequences on the plane

Details Transversal fluctuations for increasing subsequences on the plane Transversal fluctuations for increasing subsequences on the plane

1999-10-27

arxiv.org/abs/math/9910146v1

Mathematics

Probability

16 pages

Scientific paper

Consider a realization of a Poisson process in R^2 with intensity 1 and take a maximal up/right path from the origin to (N,N) consisting of line segments between the points, where maximal means that it contains as many points as possible. The number of points in such a path has fluctuations of order N^chi, where chi=1/3 by a result of Baik-Deift-Johansson. Here we show that typical deviations of a maximal path from the diagonal x=y is of order N^xi with xi=2/3. This is consistent with the scaling identity chi=2xi-1, which is believed to hold in many random growth models.

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