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We investigate quantitative aspects of the LEF property for subgroups of thetopological full group $[[ \sigma ]]$ of a two-sided minimal subshift over afinite alphabet, measured via the LEF growth function. We show that the LEFgrowth of $[[ \sigma ]]^{\prime}$ may be bounded from above and below in termsof the recurrence function and the complexity function of the subshift,respectively. As an application, we construct groups of previously unseen LEFgrowth types, and exhibit a continuum of finitely generated LEF groups whichmay be distinguished from one another by their LEF growth.

Topological full groups of minimal subshifts and quantifying local embeddings into finite groups