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Tuesday 28 May 2019, 15:00-16:00
Isomorphism theorems and the sign cluster geometry of the Gaussian free field
- 👤 Speaker: Pierre-Francois Rodriguez (IHES, Paris) 🔗 Website
- 📅 Date & Time: Tuesday 28 May 2019, 15:00 - 16:00
- 📍 Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB
Abstract
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. Prévost and A. Drewitz.
Series This talk is part of the Probability series.
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