We consider the convergence of partition functions and endpoint density for the half-space directed polymer model in dimension $1+1$ in the intermediate disorder regime as considered for the full space model by Alberts, Khanin and Quastel in [AKQ]. By scaling the inverse temperature like $\beta n^{-1/4}$, the point-to-point partition function converges to the chaos series for the solution to stochastic heat equation with Robin boundary condition and delta initial data. We also apply our convergence results to the exact-solvable log-gamma directed polymer model in a half-space.

中文翻译：

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半空间定向聚合物的中间无序机制

我们考虑了半空间定向聚合物模型在中间无序状态中维度 $1+1$ 的分配函数和端点密度的收敛性，正如 Alberts、Khanin 和 Quastel 在 [AKQ] 中对全空间模型所考虑的那样。通过像 $\beta n^{-1/4}$ 一样缩放逆温度，点对点分配函数收敛到混沌级数，用于求解具有 Robin 边界条件和 delta 初始数据的随机热方程。我们还将我们的收敛结果应用于半空间中精确可解的对数伽马定向聚合物模型。