My Research
A complete list of my preprints and publications (updated August, 2022)My main area of research is processes in random environments. Most of my research has been in random walks in random environments, but recently I have become interested in other processes (such as interacting particle systems) in random environments. I'm also interested in other non-classical random walks - especially the multi-excited random walk (also called the cookie random walk).
My Google Scholar Citation Profile.
My personal list of advice and resources for new researchers (grad students and undergrads).
Probability at Purdue
Current members of the probability group at Purdue University are- Rodrigo Banuelos
- Anirban DasGupta
- Chris Janjigian
- Takashi Owada
- Jonathon Peterson
- Thomas Sellke
- Samy Tindel
- Jing Wang
- Mark Daniel Ward
Undergraduate Research
I am the chair of the Undergraduate Research Committee in the Mathematics Department. Undergraduate students interested in doing research in mathematics can find more information at the Undergraduate Research page on the math department website. I have also directed a number of undergraduate research projects, many of which have resulted in publications by the students or presentations at a conference.- Best strategy for each team in the regular season to win championship in the knockout tournament.
Zijie (Jerry) Zhou
Published in SIAM Undergraduate Research Online, Vol 13, 2020. - On the speed of an excited asymmetric random walk.
Mike Cinkoske (Purdue), Joe Jackson (Swarthmore College), and Claire Plunkett (Case Western Reserve)
Published in the Rose-Hulman Undergraduate Mathematics Journal, Vol 19, no. 1, 2018.
Poster - Statistical tests for convergence of some random walks to perturbed Brownian motion.
Jacob Menix (Western Kentucky), and Paige Schoonover (Tennessee)
Poster - Upper and lower bounds on the speed of a one-dimensional excited random walk.
Erin Bossen (Eastern Illinois), Brian Kidd (Purdue), Owen Levin (Minnesota), Jacob Smith (Franklin College), and Kevin Stangl (UCLA)
Published (joint with Jonathon Peterson) in Involve, Vol 12, no. 1, 2019.
Poster - Reaching the NFL playoffs based on week one results: a statistical and probabilistic analysis.
Peter Boyd, Brian Kidd, Weston Phillips, and Christopher Vincent
Published in the Rose-Hulman Undergraduate Mathematics Journal, Vol 20, no. 1, 2019.
Poster - Modifications of the Colley Matrix ranking method.
Cole Manschot
Senior Thesis - The joint density of the determinant and trace of a random 2×2 matrix.
Jingdan Liu
Preprint - Roots of polynomials with random integer coefficients.
Lirong Yuan
Presentation slides - Non-transitivity in probabilistic models for ranking sports teams.
João Machado (Cornell University)
Conferences
- Together with Fabrice Baudoin, I organized a conference on stochastic analysis and related topics at Purdue University in May of 2015.
- Together with Firas Rassoul-Agha, I organized a conference on random environments at Cornell University in May of 2011.