Large deviation for dynamic model of three dimensional Young diagrams

Abstract

In this notes, we study the large deviation principle for the dynamic model of three dimensional Young diagrams, having the jump rate originally given by [10]. We employ the level-set function approach discussed in [8]. Our argument is rather heuristic by relying on the assumption of local equilibrium and the local ergodicity for slope variables. We are planning to give rigorous proofs in [4] based on a different formulation due to height functions and dimer-cover picture as in [9].