Identifier

158

Lauren Sobral

Date

2019

Document Type

Honors Thesis

Degree Name

Bachelor of Science

Major

Mathematical Sciences

Committee Chair

James T. Campbell

Committee Member

Ebenezer Olusegun George

Committee Member

Dale Bowman

Abstract

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).

Comments

Undergraduate Honor's Thesis

Library Comment

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

Notes

Data is provided by the student.

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