标题： 严格次线性坐标下的随机热方程中的精确多点关联 显示英文标题

标题： Exact Multi-Point Correlations in the Stochastic Heat Equation for Strictly Sublinear Coordinates

摘要： 我们考虑在$(1+1)$维空间中具有狄拉克初始数据和时空白噪声的随机热方程（SHE）。 我们证明了当空间坐标严格次线性时，SHE 的多点关联函数的精确大时间渐近行为。 次线性条件是最佳的，因为在空间坐标线性增长的情况下已知会发生不同的渐近行为 [Lin 2023, 定理 1.1]。 最后，我们结果的一个显著特点是它确认了 SHE 中多点关联函数与狄拉克玻色气体哈密顿量基态之间的联系。 显示英文摘要

摘要： 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 [Lin 2023, Theorem 1.1]. Lastly, a notable feature of our result is that it confirms the connection between multi-point correlations in the SHE and the ground state of the Hamiltonian of the delta-Bose gas.