Long-range self-avoiding walk converges to α-stable processes
Heydenreich, Markus
Ann. Inst. H. Poincaré Probab. Statist., Tome 47 (2011) no. 1, p. 20-42 / Harvested from Project Euclid
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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. A 21 (1988) L417–L420], who proves convergence to Brownian motion for nearest-neighbor self-avoiding walk in high dimension.
Publié le : 2011-02-15
Classification:  Self-avoiding walk,  Lace expansion,  α-stable processes,  Mean-field behavior,  82B41 
@article{1294170228,
     author = {Heydenreich, Markus},
     title = {Long-range self-avoiding walk converges to $\alpha$-stable processes},
     journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
     volume = {47},
     number = {1},
     year = {2011},
     pages = { 20-42},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1294170228}
}

Heydenreich, Markus. Long-range self-avoiding walk converges to α-stable processes. Ann. Inst. H. Poincaré Probab. Statist., Tome 47 (2011) no. 1, pp.  20-42. http://gdmltest.u-ga.fr/item/1294170228/