Abstract: We consider a model of a one-dimensional random walk in dynamic random environment that interpolates between two classical settings:

(I) The random environment is sampled at time zero only.
(II) The random environment is resampled at every unit of time.

In our model the random environment is resampled along an increasing sequence of deterministic times.

We consider both the quenched and the annealed version of the model, and look at various growth regimes for the resampling times. We prove laws of large numbers, central limit theorems and large deviation principles. We also look at the classification of transience versus recurrence.

We find that the cooling leads to very rich scaling behaviour.

Joint work with Luca Avena, Yuki Chino and Conrado da Costa.