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Sublinear Variance for Directed Last-Passage Percolation

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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.

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  1. DMA–École Normale Supérieure, 45 rue d’Ulm, 75230, Paris Cedex 5, France

    B. T. Graham

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  1. B. T. Graham
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Correspondence to B. T. Graham.

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Graham, B.T. Sublinear Variance for Directed Last-Passage Percolation. J Theor Probab 25, 687–702 (2012). https://doi.org/10.1007/s10959-010-0315-6

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  • DOI: https://doi.org/10.1007/s10959-010-0315-6

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