The survival probability for critical spread-out oriented percolation above dimensions. II. Expansion
Remco Van der Hofstad, Frank den Hollander, Gordon Slade (2007)
Annales de l'I.H.P. Probabilités et statistiques
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Remco Van der Hofstad, Frank den Hollander, Gordon Slade (2007)
Annales de l'I.H.P. Probabilités et statistiques
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Pietro Caputo, Dmitry Ioffe (2003)
Annales de l'I.H.P. Probabilités et statistiques
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Markus Heydenreich (2011)
Annales de l'I.H.P. Probabilités et statistiques
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We consider a long-range version of self-avoiding walk in dimension > 2( ∧ 2), where denotes dimension and the power-law decay exponent of the coupling function. Under appropriate scaling we prove convergence to brownian motion for ≥ 2, and to -stable Lévy motion for < 2. This complements results by Slade [ (1988) L417–L420], who proves convergence to brownian motion for nearest-neighbor self-avoiding walk in high dimension.
C. Mueller, E. Perkins (2000)
Annales de l'I.H.P. Probabilités et statistiques
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Yuji Hamana, Harry Kesten (2002)
Annales de l'I.H.P. Probabilités et statistiques
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