Séminaire de Mathématique

Convergence of double-dimers to CLE(4) via isomonodromic tau-functions

by Dmitry Chelkak (Univ. Michigan & IHES)

Centre de conférences Marilyn et James SImons (IHES)

Centre de conférences Marilyn et James SImons


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

Probability and analysis informal seminar

The main goal of this talk is to discuss a series of works (Kenyon’11, Dubédat’14, Basok-Ch.’18, Bai-Wan’21) on the convergence of double-dimer loop ensembles in Temperleyan domains to the nested CLE(4). Contrary to the convergence results available for several other lattice models in 2D (LERW/UST, critical Ising and percolation), this approach does not rely upon martingale observables for single interfaces and uses a probabilistic interpretation of a certain SL(2)-isomonodromic tau-function instead.
The plan is to start with a crash introduction on what is known/predicted for the scaling limits of loop O(N) models in 2D – even though this is not directly related to the main subject of the talk – so as to keep a bigger picture in mind and to have more room for informal questions/discussions.



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Organized by

Thierry Bodineau, Pieter Lammers, Yilin Wang