The total mass U(t) of the 2D parabolic Anderson model with white-noise potential satisfies log U(t) ~ χ t log t almost surely as t → ∞, with χ from a variational formula also governing the principal eigenvalue on expanding boxes.
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Proves existence of transition kernel and explicit upper/lower heat kernel bounds for martingale solutions to SDEs with distributional drifts of regularity > -1/2.
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Longtime asymptotics of the two-dimensional parabolic Anderson model with white-noise potential
The total mass U(t) of the 2D parabolic Anderson model with white-noise potential satisfies log U(t) ~ χ t log t almost surely as t → ∞, with χ from a variational formula also governing the principal eigenvalue on expanding boxes.
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Quantitative heat kernel estimates for diffusions with distributional drift
Proves existence of transition kernel and explicit upper/lower heat kernel bounds for martingale solutions to SDEs with distributional drifts of regularity > -1/2.