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My interests are in diffusion processes, which allows me to study abstract harmonic analysis (integrating over groups!), real 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.
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 -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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