The expectation value of the number of loops and the left-passage probability in the double-dimer model

DOI10.1007/s00220-019-03620-3zbMath1475.82004arXiv1805.03930OpenAlexW2802895252WikidataQ126666895 ScholiaQ126666895MaRDI QIDQ2288119

Nahid Ghodratipour, Shahin Rouhani

Publication date: 17 January 2020

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.03930

zbMATH Keywords

double-dimer model

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Cites Work

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• Conformal correlation functions in the Brownian loop soup
• Random walk loop soups and conformal loop ensembles
• On the asymptotics of dimers on tori
• Anisotropic growth of random surfaces in \({2+1}\) dimensions
• Level lines of Gaussian free field. I: Zero-boundary GFF.
• The complexity of computing the permanent
• Conformal invariance in random cluster models. I: Holomorphic fermions in the Ising model
• Contour lines of the two-dimensional discrete Gaussian free field
• The conformal loop ensemble nesting field
• Exact solution of the 2d dimer model: corner free energy, correlation functions and combinatorics
• Exploration trees and conformal loop ensembles
• The bead model and limit behaviors of dimer models
• A guide to stochastic Löwner evolution and its applications
• Local statistics of lattice dimers
• The Laplacian and Dirac operators on critical planar graphs
• SLEs as boundaries of clusters of Brownian loops
• Conformal field theories of stochastic Loewner evolutions
• Conformal restriction, highest-weight representations and SLE
• The Brownian loop soup
• Conformal fields, restriction properties, degenerate representations and SLE.
• Scaling limits of loop-erased random walks and uniform spanning trees
• Double dimers, conformal loop ensembles and isomonodromic deformations
• Local statistics for random domino tilings of the Aztec diamond
• A percolation formula
• Conformal invariance of domino tiling.
• Dominos and the Gaussian free field.
• Conformal loop ensembles: the Markovian characterization and the loop-soup construction
• Computability of series representations for Green's functions in a rectangle
• Tau-functions à la Dubédat and probabilities of cylindrical events for double-dimers and CLE(4)
• Convergence of Ising interfaces to Schramm's SLE curves
• Conformal invariance of loops in the double-dimer model
• SLE for theoretical physicists
• Gaussian free fields for mathematicians
• A variational principle for domino tilings
• The statistics of dimers on a lattice
• SLE and the free field: Partition functions and couplings
• Dynamic Scaling of Growing Interfaces
• DIMERS ON TWO-DIMENSIONAL LATTICES
• Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model
• Lattice Models of Polymers
• Dimer problem in statistical mechanics-an exact result
• The conformally invariant measure on self-avoiding loops
• Towards conformal invariance of 2D lattice models

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