Long-range self-avoiding walk converges to α-stable processes

Markus Heydenreich

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 1, page 20-42
  • ISSN: 0246-0203

Abstract

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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. A21 (1988) L417–L420], who proves convergence to brownian motion for nearest-neighbor self-avoiding walk in high dimension.

How to cite

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Heydenreich, Markus. "Long-range self-avoiding walk converges to α-stable processes." Annales de l'I.H.P. Probabilités et statistiques 47.1 (2011): 20-42. <http://eudml.org/doc/239654>.

@article{Heydenreich2011,
abstract = {We consider a long-range version of self-avoiding walk in dimension d &gt; 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 &lt; 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.},
author = {Heydenreich, Markus},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {self-avoiding walk; Lace expansion; α-stable processes; mean-field behavior; lace expansion; -stable processes},
language = {eng},
number = {1},
pages = {20-42},
publisher = {Gauthier-Villars},
title = {Long-range self-avoiding walk converges to α-stable processes},
url = {http://eudml.org/doc/239654},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Heydenreich, Markus
TI - Long-range self-avoiding walk converges to α-stable processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 1
SP - 20
EP - 42
AB - We consider a long-range version of self-avoiding walk in dimension d &gt; 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 &lt; 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.
LA - eng
KW - self-avoiding walk; Lace expansion; α-stable processes; mean-field behavior; lace expansion; -stable processes
UR - http://eudml.org/doc/239654
ER -

References

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