Quenched limits for sub-ballistic random walks in random conductances: high and low dimensions.

Resumen:  Consider a random walk amongst elliptic conductances with a deterministic directional bias. For all dimensions larger or equal than 2, Fribergh proved that the walk is ballistic if and only if the mean of a conductance is finite. In the infinite mean case, under proper regularity conditions, Fribergh and Kious showed the convergence of the rescaled process towards Fractional Kinetics, in the annealed setting. I will explain how to obtain a quenched limit by exploiting a celebrated idea of Bolthausen and Sznitman. I will highlight the difference between the high dimensional case (d \ge 5) and the low dimensional one (d = 2,3,4), and how one could apply our strategy to a wide class of models of biased random walks. This is based on joint works with A. Fribergh, T. Lions and U. De Ambroggio.

Posted on Nov 10, 2025 in Seminario de Probabilidades de Chile, Seminars