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- W2891080933 abstract "Building upon recent results of Dubedat (see arXiv:1403.6076) on the convergence of topological correlators in the double-dimer model considered on Temperleyan approximations $Omega^delta$ to a simply connected domain $Omegasubsetmathbb C$ we prove the convergence of probabilities of cylindrical events for the emph{double-dimer loop ensembles} on $Omega^delta$ as $deltato 0$. More precisely, let $lambda_1,dots,lambda_ninOmega$ and $L$ be a macroscopic lamination on $Omegasetminus{lambda_1,dots,lambda_n}$, i.e., a collection of disjoint simple loops surrounding at least two punctures considered up to homotopies. We show that the probabilities $P_L^delta$ that one obtains $L$ after withdrawing all loops surrounding no more than one puncture from a double-dimer loop ensemble on $Omega^delta$ converge to a conformally invariant limit $P_L$ as $delta to 0$, for each $L$. Though our primary motivation comes from 2D statistical mechanics and probability, the proofs are of a purely analytic nature. The key techniques are the analysis of entire functions on the representation variety $mathrm{Hom}(pi_1(Omegasetminus{lambda_1,dots,lambda_n})tomathrm{SL}_2(mathbb C))$ and on its (non-smooth) subvariety of locally unipotent representations. In particular, we do emph{not} use any RSW-type arguments for double-dimers. The limits $P_L$ of the probabilities $P_L^delta$ are defined as coefficients of the isomonodormic tau-function studied by Dubedat with respect to the Fock--Goncharov lamination basis on the representation variety. The fact that $P_L$ coincides with the probability to obtain $L$ from a sample of the nested CLE(4) in $Omega$ requires a small additional input, namely a mild crossing estimate for this nested conformal loop ensemble." @default.
- W2891080933 created "2018-09-27" @default.
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- W2891080933 date "2020-09-11" @default.
- W2891080933 modified "2023-09-27" @default.
- W2891080933 title "Tau-functions à la Dubédat and probabilities of cylindrical events for double-dimers and CLE(4)" @default.
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