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Transversal fluctuations for increasing subsequences on the plane
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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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Cited by 1 Pith paper
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Long-wavelength amplification of an NLS conserved-charge violation in a one-dimensional Gross-Pitaevskii-Poisson field
The full text conditionally reduces the sound-sector phase of a 1D GPP toy model to a KPZ equation; the metadata abstract describes a different Q3 charge-violation study.
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