Quenched Central Limit Theorem in a Corner Growth Setting

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.

12 pages; 3 figures; v2: corrected typos, added references and minor clarifications. To appear in Electron. Commun. Probab

References in corpus (1)

• Variational formulas, Busemann functions, and fluctuation exponents for the corner growth model with exponential weights