Lauren Sobral



Document Type

Honors Thesis

Degree Name

Bachelor of Science


Mathematical Sciences

Committee Chair

James T. Campbell

Committee Member

Ebenezer Olusegun George

Committee Member

Dale Bowman


We examine a discrete setup which loosely models various natural phenomena, including lightning formation and flow of water on an uneven surface (i.e., river delta). We fill the cells of an m x n grid with randomly-generated integers (selected from {0, 1,..., k}, say), randomly select a cell in the top row, and 'step' to neighboring cells whose values do not exceed the initial value, repeating this process starting in each new visited cell. We are interested in the fate of the resulting path, and would especially like to know the probability that some portion of the path will reach the bottom of the grid. We think of this case as success, or more colloquially, a lightning strike. We prove two basic results: changing the order of examination of the neighbors may produce different paths, but does not affect the probability of success; and the case of an m x 2 grid, with cell values chosen randomly from {1,2,...k}, may be modeled by a random walk on a tree. Moreover, using this model we obtain a recursive formula which yields the exact probability of success (in this case).


Undergraduate Honor's Thesis

Library Comment

Honors thesis originally submitted to the Local University of Memphis Honor’s Thesis Repository.


Data is provided by the student.