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Conformal restriction: the chordal and the radial

Date: 
Tuesday 16th June 2015 - 15:30 to 16:30
Venue: 
INI Seminar Room 1
Abstract: 
Co-authors: Greg Lawler (Math. Department of Chicago University), Oded Schramm (Microsoft Research), Wendelin Werner (Math. Department of ETH)

When people tried to understand two-dimensional statistical physics models, it is realized that any conformally invariant process satisfying a certain restriction property has corssing or intersection exponents. Conformal field theory has been extremely successful in predicting the exact values of critical exponents describing the bahvoir of two-dimensional systems from statistical physics. The main goal of this talk is to review the restriction property and related critical exponents. First, we will introduce Brownian intersection exponents. Second, we discuss Conformal Restriction---the chordal case and the radial case. Third, we explain the idea of the proofs. Finally, we give some relation between conformal restriction sets and intersection exponents.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons