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Extensions of the Duminil-Copin/Smirnov identity for SAWs February 28, 2012 (10:00 AM PST - 11:00 AM PST)
Parent Program: --
Location: MSRI: Simons Auditorium
Speaker(s) Anthony Guttmann (University of Melbourne)
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A recently proved identity due to Duminil-Copin and Smirnov connects different generating functions for self-avoiding walks on the honeycomb lattice. Their identity holds only at the critical step fugacity $x_c,$ and was used by them to prove that $x_c=1/(1+\sqrt{2}).$ We extend their identity off-criticality, allowing us to prove certain exponent inequalities, and to prove an identity connecting the critical exponent describing the winding-angle of SAW with the exponents for SAW in a half-plane. Other extensions are also mentioned.

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