Resumen:
The connections between random walks and electrical networks are well-known. I will describe work in this direction that demonstrates that if a sequence of spaces equipped with “resistance metrics” and measures converges with respect to the Gromov-Hausdorff -vague topology, and a certain non-explosion condition is satisfi ed, then the associated stochastic processes alsoconverge. This result generalises previous work on fractals and various models of randomgraphs in critical regimes. If time permits, I will also discuss associated time-changes and heat kernel estimates. This is partly joint work with Ben Hambly (Oxford) and Takashi Kumagai(Kyoto).