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SUMMARY:Almost sure multifractal spectrum of SLE - Gwynne\, E (Massachuset
 ts Institute of Technology)
DTSTART:20150128T100000Z
DTEND:20150128T110000Z
UID:TALK57557@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-authors: Jason Miller (Massachusetts Institute of Technolog
 y)\, Xin Sun (Massachusetts Institute of Technology) \n\nSuppose that $ta
 $ is an SLE$_kappa$ in a smoothly bounded simply connected domain $D  ubse
 t mathbb C$ and that $phi$ is a conformal map from the unit disk $mathbb D
 $ to a connected component of $D  etminus ta([0\,t])$ for some $t>0$. The
  multifractal spectrum of $ta$ is the function $(-1\,1) \nightarrow [0\,i
 nfty)$ which\, for each $s in (-1\,1)$\, gives the Hausdorff dimension of 
 the set of points $x in partial mathbb D$ such that $|phi'( (1-psilon) x)
 | = psilon^{-s+o(1)}$ as $psilon \nightarrow 0$. I will present a rigoro
 us computation of the a.s. multifractal spectrum of SLE (joint with J. Mil
 ler and X. Sun)\, which confirms a prediction due to Duplantier. The proof
  makes use of various couplings of SLE with the Gaussian free field. As a 
 corollary\, we also confirm a conjecture of Beliaev and Smirnov \nfor the 
 a.s. bulk integral means spectrum of SLE.\n
LOCATION:Seminar Room 1\, Newton Institute
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