Long-range random walks with critical jump index homogenize to Brownian motion under the scaling k^{-1} X_{k^2 (log k)^{-1} t} with resolvent convergence rate (log k)^{-1/2 + 1/(2(d-2)) + ε} for d > 3.
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Quantitative stochastic homogenization for long-range random walks with critical jump index
Long-range random walks with critical jump index homogenize to Brownian motion under the scaling k^{-1} X_{k^2 (log k)^{-1} t} with resolvent convergence rate (log k)^{-1/2 + 1/(2(d-2)) + ε} for d > 3.