Quenched Central Limit Theorem in a Corner Growth Setting
Probability
2023-11-30 v2 Mathematical Physics
Combinatorics
math.MP
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.
Cite
@article{arxiv.1804.04222,
title = {Quenched Central Limit Theorem in a Corner Growth Setting},
author = {H. Christian Gromoll and Mark W. Meckes and Leonid Petrov},
journal= {arXiv preprint arXiv:1804.04222},
year = {2023}
}
Comments
12 pages; 3 figures; v2: corrected typos, added references and minor clarifications. To appear in Electron. Commun. Probab