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SUMMARY:Critical Ising model on random triangulations of the disk: enumera
 tion and limits - Joonas Turunen (University of Helsinki)
DTSTART:20180713T083500Z
DTEND:20180713T085500Z
UID:TALK108274@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<i>In this talk\, I consider Boltzmann random triangulations c
 oupled to the Ising model on their faces\, under Dobrushin boundary condit
 ions and at the critical point. First\, the partition function&nbsp\;is co
 mputed and&nbsp\;the perimeter exponent shown to be&nbsp\;7/3&nbsp\;instea
 d of the exponent&nbsp\;5/2&nbsp\;for uniform triangulations. Then\, I ske
 tch the&nbsp\; construction of the&nbsp\;local limit in distribution when 
 the two components of the Dobrushin boundary tend to infinity one after th
 e other\,&nbsp\;using the peeling process along an Ising interface. In par
 ticular\,&nbsp\;the main interface in the local limit touches the (infinit
 e) boundary almost surely only finitely many times\, a behavior opposite t
 o that of the Bernoulli percolation on uniform maps. Some scaling limits c
 losely related to the perimeters of clusters are also discussed. This is b
 ased on a joint work with Linxiao Chen.</i>  <br><br><br><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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