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تسجيل مستخدم جديدLong-range self-avoiding walk converges to alpha-stable processes
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Markus Heydenreich
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We consider a long-range version of self-avoiding walk in dimension $d > 2(alpha wedge 2)$, where $d$ denotes dimension and $alpha$ the power-law decay exponent of the coupling function. Under appropriate scaling we prove convergence to Brownian motion for $alpha ge 2$, and to $alpha$-stable Levy motion for $alpha < 2$. 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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