Boundary-connectivity via graph theory

DOI10.1090/S0002-9939-2012-11333-4zbMath1259.05049arXiv0711.1713OpenAlexW2963081305MaRDI QIDQ4908261

Ádám Timár

Publication date: 5 March 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.1713

Mathematics Subject Classification ID

Geometric group theory (20F65) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Planar graphs; geometric and topological aspects of graph theory (05C10) Connectivity (05C40) Infinite graphs (05C63)

Related Items (25)

Formation of an interface by competitive erosion ⋮ The size of the boundary in first-passage percolation ⋮ Concentration inequalities for log-concave distributions with applications to random surface fluctuations ⋮ Measurable Hall's theorem for actions of abelian groups ⋮ Isoperimetry in supercritical bond percolation in dimensions three and higher ⋮ Rigidity of 3-colorings of the discrete torus ⋮ Borel circle squaring ⋮ Competitive erosion is conformally invariant ⋮ Algorithmic Pirogov-Sinai theory ⋮ A new look at the interfaces in percolation ⋮ Random-field random surfaces ⋮ On chemical distance and local uniqueness of a sufficiently supercritical finitary random interlacements ⋮ Collapse and diffusion in harmonic activation and transport ⋮ Odd cutsets and the hard-core model on \(\mathbb{Z}^{d}\) ⋮ Continuity for the asymptotic shape in the frog model with random initial configurations ⋮ Existence of a phase transition in harmonic activation and transport ⋮ Rigidity of proper colorings of \(\mathbb{Z}^d \) ⋮ Disconnection and level-set percolation for the Gaussian free field ⋮ The Growth Constant of Odd Cutsets in High Dimensions ⋮ Percolation of finite clusters and infinite surfaces ⋮ Phase Transition for the Speed of the Biased Random Walk on the Supercritical Percolation Cluster ⋮ Transience of the vacant set for near-critical random interlacements in high dimensions ⋮ Regularity of the time constant for a supercritical Bernoulli percolation ⋮ The time constant for Bernoulli percolation is Lipschitz continuous strictly above \(p_c\) ⋮ Quenched invariance principles for random walks and elliptic diffusions in random media with boundary

Cites Work

• Unnamed Item
• The probability of a large cluster in supercritical Bernoulli perlocation
• A note on percolation on \(\mathbb Z^d\): isoperimetric profile via exponential cluster repulsion
• Rigidity of the interface in percolation and random-cluster models
• Surface order large deviations for Ising, Potts and percolation models
• Surface order large deviations for high-density percolation
• Greedy lattice animals: geometry and criticality
• On the chemical distance for supercritical Bernoulli percolation
• ENTANGLEMENT IN PERCOLATION
• Cutsets in Infinite Graphs
• Cut sets and normed cohomology with applications to percolation

This page was built for publication: Boundary-connectivity via graph theory