Random walk spaces are a general framework for the study of PDEs.
They include as particular cases locally finite weighted connected graphs and nonlocal
settings involving symmetric integrable kernels on $\R^N$. We are interested in the study of evolution
problems involving two random walk structures so that the associated
functionals have different growth on each structure. We also deal with the case of a functional with different growth on a partition of the random walk.
Joint work with W. G\'{o}rny and J. Toledo