Superconcentration in surface growth

Height functions of growing random surfaces are often conjectured to be superconcentrated, meaning that their variances grow sublinearly in time. This article introduces a new concept—called subroughness—meaning there exist two distinct points such the expected squared difference between heights at these grows The main result paper is superconcentration equivalent subroughness class surfaces. applied establish variant restricted solid-on-solid (RSOS) model and ballistic deposition model, give proofs directed last-passage percolation polymers.