For any α<0 there exist drifts u in L^∞_t C^α_x such that the additive SDE dX=u(t,X)dt+dB has unique weak solutions but fails pathwise uniqueness.
Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift, September 2024
4 Pith papers cite this work. Polarity classification is still indexing.
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At criticality for long-range jumps with i.i.d. elliptic conductances, the model homogenizes to the Laplacian at rate 1/sqrt|ln ε|, implying sqrt(t log t) quenched scaling to Brownian motion with diffusivity given solely by the mean conductance.
Under scale-separation assumptions, the authors prove qualitative homogenization, optimal L2 convergence rates, and uniform interior/boundary Lipschitz estimates for elliptic equations with infinitely many periodic scales.
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.
citing papers explorer
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Sharp pathwise nonuniqueness for additive SDEs
For any α<0 there exist drifts u in L^∞_t C^α_x such that the additive SDE dX=u(t,X)dt+dB has unique weak solutions but fails pathwise uniqueness.
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Quantitative homogenization for the critical long-range random conductance model
At criticality for long-range jumps with i.i.d. elliptic conductances, the model homogenizes to the Laplacian at rate 1/sqrt|ln ε|, implying sqrt(t log t) quenched scaling to Brownian motion with diffusivity given solely by the mean conductance.
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Quantitative homogenization of elliptic equations with infinitely many scales
Under scale-separation assumptions, the authors prove qualitative homogenization, optimal L2 convergence rates, and uniform interior/boundary Lipschitz estimates for elliptic equations with infinitely many periodic scales.
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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.