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Beskrivning
In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits.
Introduction.- Weighted graphs and the associated Markov chains.- Heat kernel estimates – General theory.- Heat kernel estimates using effective resistance.- Heat kernel estimates for random weighted graphs.- Alexander-Orbach conjecture holds when two-point functions behave nicely.- Further results for random walk on IIC.- Random conductance model.