Long-range self-avoiding walk converges to \(\alpha\)-stable processes

DOI10.1214/09-AIHP350zbMath1210.82055arXiv0809.4333OpenAlexW2100774640MaRDI QIDQ629796

Markus Heydenreich

Publication date: 10 March 2011

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/0809.4333

zbMATH Keywords

lace expansionself-avoiding walk\(\alpha \)-stable processesmean-field behavior

Mathematics Subject Classification ID

Brownian motion (60J65) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41) Stable stochastic processes (60G52)

Related Items (8)

Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation ⋮ The survival probability and \(r\)-point functions in high dimensions ⋮ The scaling limit of the weakly self-avoiding walk on a high-dimensional torus ⋮ Asymptotic behavior of the gyration radius for long-range self-avoiding walk and long-range oriented percolation ⋮ Critical two-point function for long-range \(O(n)\) models below the upper critical dimension ⋮ Critical exponents for long-range \(\mathrm O(n)\) models below the upper critical dimension ⋮ Scaling limits and critical behaviour of the 4-dimensional \(n\)-component \(|\varphi|^4\) spin model ⋮ Self-avoiding walk, spin systems and renormalization

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