Electronic Communications in Probability

Quenched central limit theorem in a corner growth setting

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

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1545188961

Digital Object Identifier
doi:10.1214/18-ECP201

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

Keywords
last passage percolation central limit theorem concentration of measure

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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