Fluctuation universality for a class of directed solid-on-solid models

TL;DR

This paper demonstrates that fluctuations in a class of directed solid-on-solid models follow the Airy process, revealing universality in their limiting distribution across different height distributions.

Contribution

It establishes fluctuation universality for directed solid-on-solid models, extending results from uniform to general absolutely continuous height distributions.

Findings

Fluctuations follow the Airy process along the back row.

Universality holds for a broad class of height distributions.

Results connect solid-on-solid models with random matrix theory.

Abstract

Our interest is in a class of directed solid-on-solid models, which may be regarded as continuum versions of boxed plane partitions. In the case that the heights are chosen from a uniform distribution, the joint PDF of the heights is the same as that for the positions in a finitized bead process recently introduced by the authors and Nordenstam. We use knowledge of the correlation functions for the latter to show that upon a certain scaling the fluctuations of the heights along the back row of the solid-on-solid model are given by the Airy process from random matrix theory, as is the case for boxed plane partitions. Moreover, we show that this limiting distribution remains true if instead of the uniform distribution, the heights are sampled from a general absolutely continuous distribution.