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Transversal fluctuations for increasing subsequences on the plane
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  • Published: April 2000

Transversal fluctuations for increasing subsequences on the plane

  • Kurt Johansson1 

Probability Theory and Related Fields volume 116, pages 445–456 (2000)Cite this article

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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 N χ, where χ = 1/3, [BDJ]. Here we show that typical deviations of a maximal path from the diagonal x = y is of order N ξ with ξ = 2/3. This is consistent with the scaling identity χ = 2ξ− 1 which is believed to hold in many random growth models.

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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, Lindstedtsvägen 25, S-100 44 Stockholm, Sweden. e-mail: kurtjmath.kth.se, , , , , , SE

    Kurt Johansson

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  1. Kurt Johansson
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Received: 16 April 1999 / Revised version: 5 July 1999 / Published online: 14 February 2000

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Johansson, K. Transversal fluctuations for increasing subsequences on the plane. Probab Theory Relat Fields 116, 445–456 (2000). https://doi.org/10.1007/s004400050258

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  • Issue Date: April 2000

  • DOI: https://doi.org/10.1007/s004400050258

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Keywords

  • Line Segment
  • Growth Model
  • Poisson Process
  • Typical Deviation
  • Maximal Path
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