Scaling limits of (\(1+1\))-dimensional pinning models with Laplacian interaction

DOI10.1214/08-AOP424zbMath1185.60106arXiv0802.3154MaRDI QIDQ2270605

Francesco Caravenna, Jean-Dominique Deuschel

Publication date: 28 July 2009

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

Full work available at URL: https://arxiv.org/abs/0802.3154

zbMATH Keywords

phase transitionscaling limitLevy processMarkov renewal theoryBrascamp-Lieb inequalitypinning model

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41)

Related Items (17)

Pinning for the critical and supercritical membrane model ⋮ Estimates for the Green's function of the discrete Bilaplacian in dimensions 2 and 3 ⋮ Unnamed Item ⋮ The maximum of the four-dimensional membrane model ⋮ The scaling limit of the membrane model ⋮ Scaling limit of semiflexible polymers: a phase transition ⋮ Thermodynamic and scaling limits of the non-Gaussian membrane model ⋮ On the free energy of a Gaussian membrane model with external potentials ⋮ The scaling limits of a heavy tailed Markov renewal process ⋮ A shape theorem for the scaling limit of the IPDSAW at criticality ⋮ On the maximum of conditioned random walks and tightness for pinning models ⋮ Scaling limits of weakly asymmetric interfaces ⋮ Some rigorous results on semiflexible polymers. I: Free and confined polymers ⋮ Pinning and wetting transition for (1\(+\)1)-dimensional fields with Laplacian interaction ⋮ Maximum and entropic repulsion for a Gaussian membrane model in the critical dimension ⋮ The scaling limits of the non critical strip wetting model ⋮ Maximum of the membrane model on regular trees

Cites Work

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• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• Pinning and wetting transition for (1\(+\)1)-dimensional fields with Laplacian interaction
• An Elementary Characterization of Weak Convergence of Measures
• Characterisation of weak convergence of signed measures on $[0,1$.]
• Applied Probability and Queues
• Monotonicity properties of optimal transportation and the FKG and related inequalities

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