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My interests are in diffusion processes, which allows me to study abstract harmonic analysis (integrating over groups!), p-adic analysis, and probability theory. My advisor is David Weisbart. In 2020, Dr. Weisbart, published a paper ([2010.05492] $p$-Adic Brownian Motion is a Scaling Limit (arxiv.org) ) showing that p-adic diffusion is a scaling limit of discrete time random walks. My research is to see what similar processes look like in more specific p-adic settings. Additionally, I studied Representation Theory of Lie Algebras, specifically Demazure modules of Current Algebras.
Publications:
Brownian Motion in a Vector Space Over a Local Field is a Scaling Limit - [Tyler Pierce, Rahul Rajkumar, Andrea Stine, David Weisbart, Adam M. Yassine, Brownian motion in a vector space over a local field is a scaling limit, Expositiones Mathematicae, Volume 42, Issue 6, 2024, 125607, ISSN 0723-0869, https://doi.org/10.1016/j.exmath.2024.125607.
Brownian Motion in Z_p is a Limit of Discrete Time Random Walks - Pierce, T., Weisbart, D. Brownian Motion in the P-Adic Integers is a Limit of Discrete Time Random Walks. J Stat Phys 192, 104 (2025). https://doi.org/10.1007/s10955-025-03474-1
Talks:
Below is a presentation I gave on my thesis research.
My_Defense_slides7-2.pdfGoogle Sites
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