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In this paper, we study the behaviour of the longest common substring forrandom subshifts of finite type (for dynamicists) or of the longest commonsubstring for random sequences in random environments (for probabilists). Weprove that, under some exponential mixing assumptions, this behaviour is linkedto the R\'enyi entropy of the stationary measure. We emphasize that what weestablish is a quenched result.

Longest common substring for random subshifts of finite type