Quenched Central Limit Theorem in a Corner Growth Setting.

  title={Quenched Central Limit Theorem in a Corner Growth Setting.},
  author={H. C. Gromoll and Mark W. Meckes and L. Petrov},
  journal={arXiv: Probability},
  • H. C. Gromoll, Mark W. Meckes, L. Petrov
  • Published 2018
  • Mathematics, Physics
  • arXiv: Probability
  • 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. 
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