Long-range self-avoiding walk converges to α-stable processes
نویسنده
چکیده
Abstract: 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 (1988), who proves convergence to Brownian motion for nearest-neighbor self-avoiding walk in high dimension.
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