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We consider random walks amongst random conductances in the cases where theconductances can be arbitrarily small, with a heavy-tailed distribution at 0,and where the conductances may or may not have a heavy-tailed distribution atinfinity. We study the long time behaviour of these processes and prove agingstatements. When the heavy tail is only at 0, we prove that aging can beobserved for the maximum of the process, i.e.~the same maximal value isattained repeatedly over long time-scales. When there are also heavy tails atinfinity, we prove a classical aging result for the position of the walker, aswell as a sub-aging result that occurs on a shorter time-scale.

Aging and sub-aging for one-dimensional random walks amongst random conductances