Non-coincidence of quenched and annealed connective constants on the supercritical planar percolation cluster

DOI10.1007/s00440-013-0520-1zbMath1298.82030arXiv1203.6051OpenAlexW2065009430MaRDI QIDQ398783

Hubert Lacoin

Publication date: 15 August 2014

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

Full work available at URL: https://arxiv.org/abs/1203.6051

zbMATH Keywords

percolationpolymersrandom mediaself-avoiding walkdisorder relevance

Mathematics Subject Classification ID

Statistical mechanics of polymers (82D60) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Processes in random environments (60K37)

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Cites Work

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• Strong disorder in semidirected random polymers
• Self-avoiding walk is sub-ballistic
• Existence of an intermediate phase for oriented percolation
• The connective constant of the honeycomb lattice equals \(\sqrt{2+\sqrt 2}\)
• New bounds for the free energy of directed polymers in dimension \(1+1\) and \(1+2\)
• Disorder relevance at marginality and critical point shift
• Disorder relevance for the random walk pinning model in dimension 3
• On the critical point of the random walk pinning model in dimension \(d=3\)
• Differing averaged and quenched large deviations for random walks in random environments in dimensions two and three
• Directed polymers in random environment are diffusive at weak disorder
• Coarse graining, fractional moments and the critical slope of random copolymers
• Self-avoiding walk in 5 or more dimensions
• Self-avoiding walks in quenched random environments
• On the partition function of a directed polymer in a Gaussian random environment
• Existence of a non-averaging regime for the self-avoiding walk on a high-dimensional infinite percolation cluster
• Hierarchical pinning models, quadratic maps and quenched disorder
• Percolation
• Marginal relevance of disorder for pinning models