Electronic Communications in Probability

Quenched central limit theorem in a corner growth setting

H. Christian Gromoll, Mark W. Meckes, and Leonid Petrov

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We consider point-to-point directed paths in a random environment on the two-dimensional integer lattice. For a general independent environment under mild assumptions we show that the quenched energy of a typical path satisfies a central limit theorem as the mesh of the lattice goes to zero. Our proofs rely on concentration of measure techniques and some combinatorial bounds on families of paths.

Article information

Electron. Commun. Probab., Volume 23 (2018), paper no. 101, 12 pp.

Received: 3 August 2018
Accepted: 29 November 2018
First available in Project Euclid: 19 December 2018

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Digital Object Identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

last passage percolation central limit theorem concentration of measure

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Gromoll, H. Christian; Meckes, Mark W.; Petrov, Leonid. Quenched central limit theorem in a corner growth setting. Electron. Commun. Probab. 23 (2018), paper no. 101, 12 pp. doi:10.1214/18-ECP201. https://projecteuclid.org/euclid.ecp/1545188961

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