## Document Type

Honors Project - Open Access

## Abstract

A mixing measure is the expected length of a random walk on a graph given a set of starting and stopping conditions. We study a mixing measure called the forget time. Given a graph *G*, the pessimal access time for a target distribution is the expected length of an optimal stopping rule to that target distribution, starting from the worst initial vertex. The forget time of *G* is the smallest pessimal access time among all possible target distributions. We prove that the balanced double broom maximizes the forget time on the set of trees on *n* vertices with diameter *d*. We also give a precise formula for the forget time of a balanced double broom.

## Recommended Citation

Vescovo, Lola R., "The forget time for random walks on trees of a fixed diameter" (2024). *Mathematics, Statistics, and Computer Science Honors Projects*. 90.

https://digitalcommons.macalester.edu/mathcs_honors/90

#### Included in

Computer Sciences Commons, Discrete Mathematics and Combinatorics Commons, Statistics and Probability Commons

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