Random Walks

Abstract

In this chapter a review is made of the main Random walks in plane and space, and then focus on two random walks that are important to the purpose of this book: Gaussian-Dimensional Random Walk, and Markov-Dimensional Random Walk. Its definition focuses on a random process where the position at a certain moment depends only on the previous step, this particularity is called Markov condition and is essencially a Markov Chain Process. Random walks are used in simulation in different disciplines for their simplicity to handle phenomena involving several variables. Its use in physics, chemistry, ecology, biology, psychology and economics stands out. In this chapter we do not involve random walks in finite graphs since it is outside the purpose of this work. The definitions of these processes are accompanied by graphic and analytical examples.

Keywords: Gaussian-Dimensional Random Walk, Markov-Dimensional Random Walk, One-Dimensional Random Walk, Random Walks, Three-Dimensional Ramdom Walk, Two-Dimensional Random Walk

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