How quickly can we sample a uniform domino tiling of the \(2L\times 2L\) square via Glauber dynamics?

DOI10.1007/s00440-014-0553-0zbMath1328.60176arXiv1210.5456OpenAlexW1800432404MaRDI QIDQ2343025

Fabio Lucio Toninelli, Benoît Laslier

Publication date: 4 May 2015

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.5456

zbMATH Keywords

domino tilingsGlauber dynamicsperfect matchingsmean curvature motionMarkov chain algorithm

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Numerical analysis or methods applied to Markov chains (65C40) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

Related Items

The mixing time of the Lozenge tiling Glauber dynamics, Reconstruction of domino tilings -- combinatorial and probabilistic questions, Lozenge tilings, Glauber dynamics and macroscopic shape

Cites Work

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• Can extra updates delay mixing?
• Dynamics of \((2+1)\)-dimensional SOS surfaces above a wall: slow mixing induced by entropic repulsion
• Mixing times of monotone surfaces and SOS interfaces: a mean curvature approach
• Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field
• Dimers, tilings and trees
• Interface motion in models with stochastic dynamics
• Tiling of planar figures without gaps by dominos: graphical foundations of Thurston if algorithm, parallelization uniqueness and decomposion
• Generalized domino-shuffling.
• Mixing times of lozenge tiling and card shuffling Markov chains
• Conformal invariance of domino tiling.
• Dominos and the Gaussian free field.
• Trees and matchings
• Maximum matchings in planar graphs via Gaussian elimination
• Dimers and amoebae
• Height fluctuations in the honeycomb dimer model
• Analyzing Glauber dynamics by comparison of Markov chains
• Determinantal random point fields
• Markov Chain Algorithms for Planar Lattice Structures
• The statistics of dimers on a lattice
• “Zero” temperature stochastic 3D ising model and dimer covering fluctuations: A first step towards interface mean curvature motion
• Lectures on Dimers
• Dimer problem in statistical mechanics-an exact result