The conformally invariant measure on self-avoiding loops
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Abstract
We show that there exists (up to multiplicative constants) a unique and natural measure on simple loops on Riemann surfaces, such that the measure is conformally invariant and also invariant under restriction (i.e. the measure on a Riemann surface S' that is contained in another Riemann surface S, is just the measure on S restricted to those loops that stay in S'). We then study some of its properties and consequences concerning outer boundaries of critical percolation clusters and Brownian loops.Keywords
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