Rarity of extremal edges in random surfaces and other theoretical applications of cluster algorithms

DOI10.1214/20-AAP1562zbMath1460.82001arXiv1711.00259MaRDI QIDQ2657945

Ron Peled, Omri Cohen-Alloro

Publication date: 18 March 2021

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.00259

zbMATH Keywords

cluster algorithmsrandom surfacesSwendsen-Wang algorithmWolff algorithmextremal gradients

Mathematics Subject Classification ID

Classical equilibrium statistical mechanics (general) (82B05) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (4)

Concentration inequalities for log-concave distributions with applications to random surface fluctuations ⋮ Quantitative bounds on vortex fluctuations in 2d$2d$ Coulomb gas and maximum of the integer‐valued Gaussian free field ⋮ Delocalization of uniform graph homomorphisms from \({\mathbb{Z}}^2\) to \({\mathbb{Z}} \) ⋮ Power-law decay of weights and recurrence of the two-dimensional VRJP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Phase transition for the dilute clock model
• Delocalization of two-dimensional random surfaces with hard-core constraints
• Vacant set of random interlacements and percolation
• Percolation in strongly correlated systems
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• Discontinuity of the spin-wave stiffness in the two-dimensional \(XY\) model
• Percolation and the hard-core lattice gas model
• Motion by mean curvature from the Ginzburg-Landau \(\nabla\phi\) interface model
• Phase structure of two-dimensional spin models and percolation
• The sign clusters of the massless Gaussian free field percolate on \(\mathbb{Z}^{d}\), \(d \geqslant 3\) (and more)
• A uniqueness condition for Gibbs measures, with application to the 2- dimensional Ising antiferromagnet
• New results on measures of maximal entropy
• Correlation inequalities and contour estimates
• On the slow decay of \(O(2)\) correlations in the absence of topological excitations: Remark on the Patrascioiu-Seiler model
• Percolation in strongly correlated systems: The massless Gaussian field
• Phase transition and level-set percolation for the Gaussian free field
• Exponential decay of correlations in the \(2D\) random field Ising model
• Random cluster dynamics for the Ising model is rapidly mixing
• The isotropicO(3) model and the Wolff representation
• Swendsen--Wang Is Faster than Single-Bond Dynamics
• Long range correlation inequalities for massless Euclidean fields

This page was built for publication: Rarity of extremal edges in random surfaces and other theoretical applications of cluster algorithms