4 problems

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Bourgain–Spencer regularity conjecture for homogenized coefficients
Bourgain–Spencer conjecture. Under suitable mixing conditions on the random coefficient field $\boldsymbol a$ , such an operator $B_0$ exists and its Fourier symbol $\hat B_0$ is of…
Conjectureopenfourier-analysis random-coefficients stochastic-homogenizationarXiv posted 2 days ago
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Spencer's optimal decay-rate conjecture for the averaged Green's function
Spencer's conjecture. The optimal decay rate in this estimate should be $-3d$ .
Conjectureopendecay-estimates elliptic-equations random-coefficientsarXiv posted 2 days ago
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Conjecture on the optimal decay rate in the quantitative homogenization theorem
Theorem concerns the decay, as $\varepsilon\to0$ , of the error between the averaged solution and the solution of the homogenized parabolic equation in spatial dimension $d$ . Optima…
Conjectureopenparabolic-equations quantitative-homogenization random-coefficientsarXiv posted 2 days ago
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Identification with a multivariate unobservable in the triangular treatment effect model
The model has a treatment indicator $D$ , observed outcome $Y$ , covariates $X$ , instrument $V$ , and an unobservable $\Theta$ . The preceding result identifies distributions and condi…
Conjectureopencausal-inference identification random-coefficientsarXiv posted 2 days ago

Bourgain–Spencer regularity conjecture for homogenized coefficients