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This article describes the quenched localisation behaviour of the Bouchaudtrap model on the integers with regularly varying traps. In particular, itestablishes that for almost every trapping landscape there exist arbitrarilylarge times at which the system is highly localised on one site, and alsoarbitrarily large times at which the system is completely delocalised.

Quenched localisation in the Bouchaud trap model with regularly varying traps