Date of Submission
Spring 2016
Academic Programs and Concentrations
Mathematics
Project Advisor 1
Amir Barghi
Abstract/Artist's Statement
A Markov chain is said to have a cutoff if its convergence to stationary distribution exhibits a sharp threshold. In this senior project we want to determine whether lamplighter Markov chains with prisms as underlying graphs have a cutoff. Lamplighter chains describe the stochastic process of a random walk on a graph along with the mixing of {0, 1} configurations over all vertices. A prism is defined as the Cartesian product of a cycle and a path. We provide bounds of the cover time of random walk on prisms. We run computer simulations to investigate the topic empirically. We also prove theorems about pre-cutoff, which is a weaker condition than cutoff. Finally we give the conjecture that lamplighter Markov chains on prisms have pre-cutoff but no cutoff.
Access Agreement
On-Campus only
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Recommended Citation
Song, Zexi, "Cutoff for Lamplighter Markov Chains on Prisms" (2016). Senior Projects Spring 2016. 24.
https://digitalcommons.bard.edu/senproj_s2016/24
This work is protected by a Creative Commons license. Any use not permitted under that license is prohibited.
Bard Off-campus DownloadBard College faculty, staff, and students can login from off-campus by clicking on the Off-campus Download button and entering their Bard username and password.