Department of Mathematics and Statistics

Jan De Gier



ANZAMP symposium

Probability in statistical mechanics

Melbourne, 17 January 2014


Program
10-11am: Rick Kenyon (Brown University)
Limit shapes for random surfaces

I will discuss the analytic solution to the limit shape problem for random domino tilings and "lozenge" tilings, and in particular try to explain how these limiting surfaces develop facets.


11:30am-12:30pm: Wendelin Werner (ETH Zurich)
Phase transitions and conformal invariance within planar fractal carpets

It is now known for a number of models of statistical physics in two dimensions (such as percolation or the Ising model) that at their critical point, they do behave in a conformally invariant way in the large-scale limit, and do give rise in this limit to random fractals that can be mathematically described via Schramm's Stochastic Loewner Evolutions.

The goal of the present talk will be to discuss some aspects of what remains valid or should remain valid about such models and their conformal invariance, when one looks at them within a fractal-type planar domain. We shall in particular describe (and characterize) a continuous percolation interface within certain particular random fractal carpets. Part of this talk will be based on joint work with Jason Miller and Scott Sheffield.



Organiser: Jan De Gier
Contact: jdgier@unimelb.edu.au
Address: Department of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia

Venue
AMSI Access Grid Room
Building 161,
Parkville Campus
The University of Melbourne
VIC 3010
Australia

Registration
Participation is free. If you plan to attend or participate via Access Grid, please register by sending an email to agr@amsi.org.au with a CC to mshaw@amsi.org.au.

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