Height fluctuations for lozenge tilings with arbitrary "liquid" limit shape

VIENNA PROBABILITY SEMINAR

It is usual to see lozenge tilings (or more generally the dimer model) as a random surface embedded in R^3 so the question of the fluctuations of this surface is one of the most natural in the model. Many papers have studied these fluctuations using different techniques but all results until now have been limited in the types of surfaces that can appear. In this talk I will show how a new analysis based on uniform spanning trees (developed with N. Berestycki and G. Ray) combined with old ideas of Kenyon can be used to obtain the first result which does not have strong restrictions on the possible limit shape.