2023/04/14 by Timothy Sudijono, Sudijono, Timothy
Mathematics · Physics and Astronomy · #60K35 #82C41 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2304.07160
openalex publication_date 2023/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The restricted solid-on-solid (RSOS) model is a model of continuous-time surface growth characterized by the constraint that adjacent height differences are bounded by a fixed constant. Though the model is conjectured to belong to the KPZ universality class, mathematical progress on the model is very sparse. We study basic properties of the model and establish bounds on surface height fluctuations as a function of time. A linear fluctuation bound is proven for all dimensions, and a logarithmic fluctuation lower bound is given for dimension one. The proofs rely on a new characterization of RSOS as a type of first passage percolation on a disordered lattice, which is of independent interest. The logarithmic lower bound is established by showing equality in distribution to the minimum of a certain dual RSOS process.