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Central limit theorem for first-passage percolation time across thin cylinders
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  • Published: 12 June 2012

Central limit theorem for first-passage percolation time across thin cylinders

  • Sourav Chatterjee1 &
  • Partha S. Dey1 

Probability Theory and Related Fields volume 156, pages 613–663 (2013)Cite this article

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Abstract

We prove that first-passage percolation times across thin cylinders of the form [0, n] × [−h n , h n ]d-1 obey Gaussian central limit theorems as long as h n grows slower than n 1/(d+1). It is an open question as to what is the fastest that h n can grow so that a Gaussian CLT still holds. Under the natural but unproven assumption about existence of fluctuation and transversal exponents, and strict convexity of the limiting shape in the direction of (1, 0, . . . , 0), we prove that in dimensions 2 and 3 the CLT holds all the way up to the height of the unrestricted geodesic. We also provide some numerical evidence in support of the conjecture in dimension 2.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012-1185, USA

    Sourav Chatterjee & Partha S. Dey

Authors
  1. Sourav Chatterjee
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  2. Partha S. Dey
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Correspondence to Sourav Chatterjee.

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Chatterjee, S., Dey, P.S. Central limit theorem for first-passage percolation time across thin cylinders. Probab. Theory Relat. Fields 156, 613–663 (2013). https://doi.org/10.1007/s00440-012-0438-z

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  • Received: 08 December 2009

  • Revised: 14 May 2012

  • Published: 12 June 2012

  • Issue Date: August 2013

  • DOI: https://doi.org/10.1007/s00440-012-0438-z

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Keywords

  • First-passage percolation
  • Central limit theorem
  • Cylinder percolation

Mathematics Subject Classification (2000)

  • Primary 60F05
  • 60K35
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