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Consider a stochastic heat equation
=
2+() for a space–time white noise and a constant >0. Under some suitable conditions on the initial function 0 and , we show that the quantities lim sup →∞−1sup ∈ln E(|
()|2) and lim sup →∞−1ln E(sup ∈|
()|2) are equal, as well as bounded away from zero and infinity by explicit multiples of 1/. Our proof works by demonstrating quantitatively that the peaks of...
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