Last passage percolation in an exponential environment with discontinuous rates

Ciech, Federico and Georgiou, Nicos (2021) Last passage percolation in an exponential environment with discontinuous rates. Annales de l’Institut Henri Poincaré, 57 (4). pp. 2165-2188. ISSN 2308-5827

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Abstract

We prove a strong law of large numbers for directed last passage times in an independent but inhomogeneous exponential environment. Rates for the exponential random variables are obtained from a discretisation of a speed function that may be discontinuous on a locally finite set of discontinuity curves. The limiting shape is cast as a variational formula that maximises a certain functional over a set of weakly increasing curves.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
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Date Deposited: 16 Jun 2021 07:50
Last Modified: 21 Feb 2022 11:31
URI: http://sro.sussex.ac.uk/id/eprint/89732

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Project NameSussex Project NumberFunderFunder Ref
The flat edge in last passage percolationG2031EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCILEP/P021409/1