A Note on the Diffusive Scaling Limit for a Class of Linear Systems

TL;DR

This paper extends the diffusive scaling limit results for a class of linear stochastic growth models on lattices, including potlatch and smoothing processes, demonstrating broader applicability of the previous CLT findings.

Contribution

It broadens the class of models for which the diffusive scaling limit and CLT are valid, covering additional growth processes.

Findings

Diffusive scaling limit applies to wider class of models

Includes potlatch and smoothing processes

Extends previous CLT results

Abstract

We consider a class of continuous-time stochastic growth models on $d$-dimensional lattice with non-negative real numbers as possible values per site. We remark that the diffusive scaling limit proven in our previous work [Nagahata, Y., Yoshida, N.: Central Limit Theorem for a Class of Linear Systems, Electron. J. Probab. Vol. 14, No. 34, 960--977. (2009)] can be extended to wider class of models so that it covers the cases of potlatch/smoothing processes.