Transversal fluctuations for increasing subsequences on the plane

  title={Transversal fluctuations for increasing subsequences on the plane},
  author={Kurt Johansson},
  journal={Probability Theory and Related Fields},
  • K. Johansson
  • Published 27 October 1999
  • Mathematics
  • Probability Theory and Related Fields
Abstract. Consider a realization of a Poisson process in ℝ2 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 Nχ, where χ = 1/3, [BDJ]. Here we show that typical deviations of a maximal path from the diagonal x = y is of order Nξ with ξ = 2/3. This is consistent with the scaling identity χ = 2ξ− 1… 
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