Abstract
This thesis studies a model called random walk in random conductances. In particular, we study this stochastic process when the conductances and/or their inverse are regularly varying with infinite first moment. We analyse both the isotrpic model and the one with directional transience.Our hypothesis on the conductances creates slowdown phenomena such as sub-ballisticity and sub-diusivity. We rigorously derive the quenched scaling limits of this model in various dimension. Moreover, we describe the slowdown precisely in dimension one by proving several aging statements.
Our results build on previous work of [KK84, Cer11, FK18, BS20] that analysed our model in the annealed setting. In order to prove the results we implement some established techniques. In particular, in dimension one we use the theory of random walks in resistance forms developed in [Cro18, CHK17]. In higher dimensions we use the classical technique due to [BS02] that considers two independent random walks in the same random environment.
| Date of Award | 13 Sept 2023 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Daniel Kious (Supervisor) & Alexandre De Oliveira Stauffer (Supervisor) |