  Nonequilibrium fluctuations of a tagged, or distinguished particle in a class
of one dimensional mean-zero zero-range systems with sublinear, increasing
rates are derived. In Jara-Landim-Sethuraman (2009), processes with at least
linear rates are considered. A different approach to establish a main "local
replacement" limit is required for sublinear rate systems, given that their
mixing properties are much different. The method discussed also allows to
capture the fluctuations of a "second-class" particle in unit rate, symmetric
zero-range models.
