On Simple Symmetric Random Walk in -Dimensional Integer Lattice

**ABSTRACT:**

This paper analyzes a simple symmetric random walk with finite steps in d-dimensional integer lattice, ℤ and introduces one of its applications. It focuses on the total number of ways in which the walk can be accomplished. The number of ways of accomplishment is used to find the probabilities associated with all possible outcomes as a generalization of the probability associated with return to origin. In addition, the paper discusses on the total number of possible outcomes. (Since the walk is executed in ℤ , all the outcomes are integer points.) It provides an insight into the distribution of the integer lattice, ℤ .

**KEYWORDS: **allowed outcomes, fundamental integer lattice, initial condition, probability distribution function, simple symmetric random walk, Subject Classification Code (2010): 03G10, 60G50, 82B41

**DOI:**http://dx.doi.org/10.22147/jusps-A/291001

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This paper analyzes a simple symmetric random walk with finite steps in d-dimensional integer lattice, ℤ and introduces one of its applications. It focuses on the total number of...