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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Displaying similar documents to “Convergence of critical oriented percolation to super-brownian motion above dimensions”
The survival probability for critical spread-out oriented percolation above dimensions. II. Expansion
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Annales de l'I.H.P. Probabilités et statistiques
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Long-range self-avoiding walk converges to α-stable processes
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.
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