Transition density asymptotics for some diffusion processes with multi-fractal structures.
Random walks on Galton-Watson trees with infinite variance offspring distribution conditioned to survive.
Symmetric jump processes : localization, heat kernels and convergence
We consider symmetric processes of pure jump type. We prove local estimates on the probability of exiting balls, the Hölder continuity of harmonic functions and of heat kernels, and convergence of a sequence of such processes.
Uniqueness of Brownian motion on Sierpiński carpets
We prove that, up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpi´nski carpet that is invariant with respect to the local symmetries of the carpet. Consequently, for each such fractal the law of Brownian motion is uniquely determined and the Laplacian is well defined.
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