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SUMMARY:Liouville Brownian motion and thick points of the Gaussian free fi
 eld - Henry Jackson\, Cambridge
DTSTART:20150217T160000Z
DTEND:20150217T170000Z
UID:TALK58106@talks.cam.ac.uk
CONTACT:John Shimmon
DESCRIPTION:We find a lower bound for the Hausdorff dimension that a Liouv
 ille Brownian motion spends in alpha-thick points of the Gaussian Free Fie
 ld\, where Alpha is not necessarily equal to the parameter used in the con
 struction of the geometry. This completes a conjecture by N. Berestycki\, 
 where the corresponding upper bound was shown.\nIn the course of the proof
 \, we obtain estimates on the (Euclidean) diffusivity exponent\, which dep
 ends strongly on the nature of the starting point. For a Liouville typical
  point\, it is 1/(1-gamma^2/2). In particular\, for gamma > sqrt(2). the p
 ath is Lebesgue-almost everywhere differentiable\, almost surely. This pro
 vides a detailed description of the multifractal nature of Liouville Brown
 ian motion. 
LOCATION:MR12\, CMS
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