Quenched localisation in the Bouchaud trap model with regularly varying traps (Stochastic Analysis on Large Scale Interacting Systems)

"Stochastic Analysis on Large Scale Interacting Systems". October 26～29, 2015. edited by Ryoki Fukushima, Tadahisa Funaki, Yukio Nagahata, Makoto Nakashima, Hirofumi Osada and Yoshiki Otobe. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.This article describes the quenched localisation behaviour of the Bouchaud trap model on the integers with regularly varying traps. In particular, it establishes that for almost every trapping landscape there exist arbitrarily large times at which the system is highly localised on one site, and also arbitrarily large times at which the system is completely delocalised