关键词: 随机游走, 高维空间, 中心极限定理, 概率密度函数

Abstract:  Random walks are one of the classical models studied in physics, which can be applied to multiple physical problems, even in other fields. However, most textbooks concerning this topic may use complicated math methods or introduce unnecessary approximations when calculating the result. In this paper, the random walk probability density function of one particular direction is derived using the central limit theorem under many steps approximation. The radial probability density function can be derived using the result above and introducing the isotropic postulation. 

Key words: random walk, multidimensional space, central limit theorem, probability density function