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Seminar of Chebyshev Laboratory on Probability Theory
April 5, 2011 11:30, St. Petersburg, 14 line VO, 29B


Conformally invariant measure on self-avoiding loops

Stephane Benoist

Ècole Normale Supérieure, Paris

Abstract: We'll present the following result of Wendelin Werner. There exists a unique (up to multiplication by constants) and natural measure on simple loops in the plane and on each Riemann surface, 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 $S'$).

Language: English


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