Session S04 - Random Walks and Related Topics

Friday, July 16, 11:40 ~ 12:10 UTC-3

Critical exponents for a percolation model on transient graphs induced by random walks

Alexander Drewitz

Universität zu Köln, Germany   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this setup and the strong Markov property of the field on the one hand, and the links with potential theory for the associated diffusion on the other, we rigorously determine the behavior of various key quantities related to the (near-)critical regime for this model. In particular, our results apply in case the base graph is the three-dimensional cubic lattice. They unveil the associated critical exponents, which are explicit but not mean-field and consistent with predictions from scaling theory below the upper-critical dimension.

Joint work with Alexis Prévost (U Cambridge) and Pierre-François Rodriguez (Imperial College).

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