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As a matter of fact, serving as one of the power methods to describe stochastic process, random walk theoretical analysis incorporating with Monte Carlo simulations are widely applied in various fields. With this in mind, this study will discuss the principle and the state-of-art applications in three specific fields. In detail, this study will demonstrate the use of random walk as a tool in different fields: computer science, physics, and mathematics. By discussing the personalized PageRank, the random walk particle tracking method as well as the random walk simulation to solve partial differential equations. According to the analysis, this study summarized and illustrates the significance of random walk and its wide applications. At the same time, the limitations for current advance processes will be demonstrated and the prospect for improvement of the random walk simulations will be proposed. Overall, these results shed light on guiding further exploration of random walk applications in different fields.
Jonathan Yang (Fri,) studied this question.