Probability Seminar: Nathanaël Berestycki
Topic
Critical exponents for FK random planar maps
Speakers
Details
We consider random planar maps weighted by the critical Fortuin--Kasteleyn percolation model with parameter $q \in (0,4)$. The study of these surfaces is central to the theory of Liouville quantum gravity.
We obtain rigorously the value of critical exponents associated with the length of cluster
interfaces, which is shown to be $$ \frac{4}{\pi} \arccos \left( \frac{\sqrt{2 - \sqrt{q}}}{2} \right).$$ This is consistent with physics predictions; in particular, applying
the KPZ formula we recover the dimension of SLE curves.
Joint work with Benoit Laslier and Gourab Ray (Cambridge).
We obtain rigorously the value of critical exponents associated with the length of cluster
interfaces, which is shown to be $$ \frac{4}{\pi} \arccos \left( \frac{\sqrt{2 - \sqrt{q}}}{2} \right).$$ This is consistent with physics predictions; in particular, applying
the KPZ formula we recover the dimension of SLE curves.
Joint work with Benoit Laslier and Gourab Ray (Cambridge).
Additional Information
Location: ESB 2012
Nathanaël Berestycki, University of Cambridge
Nathanaël Berestycki, University of Cambridge