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Oren Louidor (Technion)
Tuesday 02 June 2015, 16:30-17:30
The full extremal process of the discrete Gaussian free field in 2D
- 👤 Speaker: Oren Louidor (Technion)
- 📅 Date & Time: Tuesday 02 June 2015, 16:30 - 17:30
- 📍 Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB
Abstract
We show the existence of the limit of the full extremal process of the discrete Gaussian free field in 2D with zero boundary conditions. The limit is a clustered Poisson point process with a random intensity measure, which is conjecturally related to the critical Liouville quantum gravity measure w.r.t. the continuous Gaussian free field. Several corollaries follow directly, e.g. a natural construction for the super-critical Gaussian multiplicative chaos and Poisson-Dirichlet statistics for the limiting Gibbs measure – both w.r.t. the CGFF . The proof is based on a novel concentric decomposition of the DGFF which effectively reduces the problem to that of finding asymptotics for the probability of a decorated non-homogenous random-walk required to stay positive. Entropic repulsion plays a key role in the analysis. Joint work with M. Biskup (UCLA)
Series This talk is part of the Probability series.
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