Random walk with Brownian motion: Theory and application

While physical models are classical, random walks are statistical models. Historically, Karl Pearson was the first to propose the random walk. This study will focus on the essential of the random walk, and additionally, this essay will offer some application guidelines and explain when the random walk is applicable. The random walk means that the performance of an event is based on the past, as people cannot predict the future development steps and directions. The random walk, which dates to the 16th century, is a significant area of probability with many applications. The random walk and Brownian motion are the main topics of this paper. The four applications of random walks that are highlighted in this paper are the following. They include the multi-particle random walk immune algorithm, the density peak clustering algorithm, a review of random walk-based community discovery techniques, and interactive image segmentation that combines random walk and random forest. This work paves the way to unravel the importance of random walk.