We consider the Stochastic Heat Equation (SHE) in (1+1) dimensions with delta Dirac initial data and spacetime white noise. We prove exact large-time asymptotics for multi-point correlations of the SHE for strictly sublinear space coordinates. The sublinear condition is optimal, in the sense that different asymptotics are known to occur when the space coordinates grow linearly Lin23, Theorem 1.1. A notable feature of our result is that the dependence on space coordinates of the SHE's asymptotic multi-point correlations is given by the ground state of the delta-Bose gas.
Lamarre et al. (Mon,) studied this question.
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