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Height gaps of planar Brownian motion and Brownian loop soup

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SSDW01 - Self-interacting processes

This talk will be focused on two recent results with Titus Lupu and Wei Qian where we derive height gap properties of certain fields across CLE /SLE loops. The first result below can be heuristically thought of as a limiting case of the second result. Firstly, we show that the occupation measure of planar Brownian motion exhibits a constant height gap of 5/π across its outer boundary. Secondly, we construct a field naturally coupled with a subcritical Brownian loop soup and show that it exhibits a constant height gap across CLE κ loops. This latter result is a generalisation of the celebrated results of Schramm—Sheffield and Miller—Sheffield concerning the height gap of the Gaussian free field across SLE4 /CLE4 curves.

This talk is part of the Isaac Newton Institute Seminar Series series.

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