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- W2025703969 abstract "We consider the parabolic Anderson problem $partial_{t}u = kappaDelta u + xi(x)u$ on $mathbb{R}_+ times mathbb{R}^d$ with initial condition $u(0, x) = 1$. Here $xi(cdot)$ is a random shift-invariant potential having high $delta$-like peaks on small islands. We express the second-order asymptotics of the $p$th moment $(p in [1, infty))$ of $u(t,0)$ as $t to infty$ in terms of a variational formula involving an asymptotic description of the rescaled shapes of these peaks via their cumulant generating function. This includes Gaussian potentials and high Poisson clouds." @default.
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- W2025703969 title "Moment asymptotics for the continuous parabolic Anderson model" @default.
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- W2025703969 doi "https://doi.org/10.1214/aoap/1019737669" @default.
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