Supercritical self-avoiding walks are space-filling

DOI10.1214/12-AIHP528zbMath1292.60096arXiv1110.3074MaRDI QIDQ2451100

Gady Kozma, Ariel Yadin, Hugo Duminil-Copin

Publication date: 26 May 2014

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.3074

zbMATH Keywords

connective constantself avoiding walk

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Combinatorial probability (60C05) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41)

Related Items (11)

Self-avoiding walk on the complete graph ⋮ Macroscopic loops in the loop \(O(n)\) model at Nienhuis' critical point ⋮ Self-avoiding walk is sub-ballistic ⋮ Interacting self-avoiding polygons ⋮ Mean-field tricritical polymers ⋮ Self‐avoiding walk on the hypercube ⋮ Weakly self-avoiding walk on a high-dimensional torus ⋮ Shifted critical threshold in the loop \(O(n)\) model at arbitrarily small \(n\) ⋮ Strongly correlated random interacting processes. Abstracts from the workshop held January 28 -- February 3, 2018 ⋮ Random permutations of a regular lattice ⋮ Scaling limit of ballistic self-avoiding walk interacting with spatial random permutations

Cites Work

• Self-avoiding walk is sub-ballistic
• The connective constant of the honeycomb lattice equals \(\sqrt{2+\sqrt 2}\)
• Functional integral representations for self-avoiding walk
• Self-avoiding walk in 5 or more dimensions
• Self-avoiding walk in five or more dimensions. I: The critical behaviour
• The Strong Interaction Limit of Continuous-Time Weakly Self-Avoiding Walk
• Renormalisation group analysis of weakly self-avoiding walk in dimensions four and higher
• Critical behaviour of self-avoiding walk in five or more dimensions
• Percolation
• Towards conformal invariance of 2D lattice models
• Lectures on Self-Avoiding Walks
• FURTHER RESULTS ON THE RATE OF CONVERGENCE TO THE CONNECTIVE CONSTANT OF THE HYPERCUBICAL LATTICE
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