Sublinear Variance for Directed Last-Passage Percolation

B. T. Graham ()
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B. T. Graham: DMA–École Normale Supérieure

Journal of Theoretical Probability, 2012, vol. 25, issue 3, 687-702

Abstract: Abstract A range of first-passage percolation type models are believed to demonstrate the related properties of sublinear variance and superdiffusivity. We show that directed last-passage percolation with Gaussian vertex weights has a sublinear variance property. We also consider other vertex weight distributions. Corresponding results are obtained for the ground state of the “directed polymers in a random environment” model.

Keywords: Directed last-passage percolation; Directed polymers in a random environment; Sublinear variance; Concentration; Strict convexity; 60K35; 82B41 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10959-010-0315-6

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