3 problems

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Huang–Lê's spatial asymptotic conjecture for the parabolic Anderson model
Let $u(t,x)$ solve the one-dimensional parabolic Anderson model with space-time white noise $xi$ and narrow wedge initial condition: … For fixed $t>0$ , Huang–Lê's spatial asymptoti…
Conjectureopenparabolic-anderson-model spatial-asymptotics stochastic-pdesarXiv posted 2 days ago
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Conjecture on spatial behavior governed by the comparison with the constant-initial-data solution
Spatial-behavior comparison conjecture. The spatial behaviors of $u_\theta(t,x)$ depend on the relation between $\log \hat{u}_\theta(t,x)$ and $\log(p_t\ast u_0)(x)$ when $|x|$ is…
Conjectureopenspatial-asymptotics stochastic-pdesarXiv posted 2 days ago
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Spatial asymptotic conjecture for the stochastic heat equation with compactly supported initial data
Spatial asymptotic conjecture. In the particular case of space-time white noise,
Conjectureopenspatial-asymptotics stochastic-heat-equation stochastic-pdesarXiv posted 2 days ago

Huang–Lê's spatial asymptotic conjecture for the parabolic Anderson model