标题： 关于具有限制角度的二维随机游走的分布 显示英文标题

标题： On the Distribution of a Two-Dimensional Random Walk with Restricted Angles

摘要： 在本文中，我们推导了二维（复数）随机游走的分布，其中每一步的角度被限制在圆周的一个子集内。这种设置出现在多个领域，例如信号处理中的空中计算。特别是，我们推导了两步的精确联合和边缘分布，对于一般步数的数值解，以及对于大量步数的近似解。此外，我们提供了任意步数的支持的精确表征。本工作中的结果为未来涉及此类问题的研究提供了参考。 显示英文摘要

摘要： In this paper, we derive the distribution of a two-dimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in signal processing. In particular, we derive the exact joint and marginal distributions for two steps, numerical solutions for a general number of steps, and approximations for a large number of steps. Furthermore, we provide an exact characterization of the support for an arbitrary number of steps. The results in this work provide a reference for future work involving such problems.