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University of Cambridge > Talks.cam > Probability > Isomorphism theorems and the sign cluster geometry of the Gaussian free field

## Isomorphism theorems and the sign cluster geometry of the Gaussian free fieldAdd to your list(s) Download to your calendar using vCal - Pierre-Francois Rodriguez (IHES, Paris)
- Tuesday 28 May 2019, 15:00-16:00
- MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
If you have a question about this talk, please contact Perla Sousi. We consider the Gaussian free field (GFF) on a large class of transient weighted graphs G, and prove that its sign clusters contain an infinite connected component. In fact, we show that the sign clusters fall into a regime of strong supercriticality, in which two infinite sign clusters dominate (one for each sign), and finite sign clusters are necessarily tiny, with overwhelming probability. Examples of graphs G belonging to this class include cases in which the random walk on G exhibits anomalous diffusive behavior. Among other things, our proof exploits a certain relation (isomorphism theorem) relating the GFF to random interlacements, which form a Poissonian soup of bi-infinite random walk trajectories. Our findings also imply the existence of a nontrivial percolating regime for the vacant set of random interlacements on G. Based on joint work with A. PrÃ©vost and A. Drewitz. This talk is part of the Probability series. ## This talk is included in these lists:- All CMS events
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