Local sub-Gaussian estimates on graphs: The strongly recurrent case.
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Localization and delocalization of random interfaces.
Velenik, Yvan (2006)
Probability Surveys [electronic only]
Long-range self-avoiding walk converges to α-stable processes
Markus Heydenreich (2011)
Annales de l'I.H.P. Probabilités et statistiques
We consider a long-range version of self-avoiding walk in dimension d > 2(α ∧ 2), where d denotes dimension and α the power-law decay exponent of the coupling function. Under appropriate scaling we prove convergence to brownian motion for α ≥ 2, and to α-stable Lévy motion for α < 2. This complements results by Slade [J. Phys. A21 (1988) L417–L420], who proves convergence to brownian motion for nearest-neighbor self-avoiding walk in high dimension.
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