Graduation Year

2023

Date of Submission

4-2023

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Reader 1

Sarah Cannon

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Terms of Use for work posted in Scholarship@Claremont.

Abstract

As of now there is no universal quantitative measure used to evaluate racial segregation in different regions. This paper begins by providing a history of segregation, with an emphasis on the impact of redlining in the early 20th century. We move to its effect on the current population distribution in Los Angeles, California, and then provide an overview of the mathematical concepts that have been used in previous measurements of segregation. We then introduce a method that we believe encompasses the most representative aspects of preceding work, proposed by Sousa and Nicosia in their work on quantifying ethnic segregation in cities using random walks: Given a graph with racial population information at each node, this method conducts a random walk and outputs the number of steps it takes to reach all racial groups in the system. In analyzing the amount of time the walk takes, we are able to form conclusions about the levels of segregation present in the region. We argue that this measure is more effective than those used previously because of its high explanatory power and preservation of graph structure. We applied this method to LA County with data collected from the U.S. 2020 Census, and found that there is a significant difference between the average step length of LA County vs. the average step length of an unbiased null model. The impacts of this study imply that LA County is racially segregated in comparison to a given neutral null model.

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