On the Wasserstein space over a complete, separable, non-compact, locally compact length space, we consider the horo-functions associated to sequences of atomic measures. We show the existence of co-rays for any prescribed initial probability measure with respect to a sequence of atomic measures and show that co-rays are negative gradient curves in some sense. Some other fundamental results of this kind of functions are also obtained.

中文翻译：

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与 Wasserstein 空间上的原子序列相关的 Horo 函数

在完整的、可分离的、非紧缩的、局部紧缩长度空间上的 Wasserstein 空间上，我们考虑与原子度量序列相关的 horo-functions。我们展示了关于一系列原子度量的任何规定的初始概率度量的共射线的存在，并表明共射线在某种意义上是负梯度曲线。还得到了这类函数的一些其他基本结果。