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SUMMARY:External DLA on a spanning-tree-weighted random planar map - Joshu
 a Pfeffer (Massachusetts Institute of Technology)
DTSTART:20180720T124500Z
DTEND:20180720T130500Z
UID:TALK108349@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:External diffusion limited aggregation (DLA) is a widely studi
 ed   subject in the physics literature\, with many manifestations in natur
 e\; but it is   not well-understood mathematically in any environment. We 
 consider external   DLA on an infinite spanning-tree-weighted random plana
 r map. We prove that the   growth exponent for the external diameter of th
 e DLA cluster exists and is equal   to $2/d _{\\sqrt{2}}$\, where $d_{\\sq
 rt{2}}$ denotes the ``fractal dimension   of $\\sqrt{2}$-Liouville quantum
  gravity (LQG)&#39\;&#39\;---or\, equivalently\, the ball   volume growth 
 exponent for the spanning-tree weighted map. Our proof is based   on the f
 act that the complement of an external DLA cluster on a spanning-tree   we
 ighted map is a spanning-tree weighted map with boundary\, which allows   
 us to reduce our problem to proving certain estimates for distances in ran
 dom   planar maps with boundary. This is joint work with Ewain Gwynne.  <b
 r><br><br><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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