Research
Research
About Me
The initial phase of my post-graduate career spanned about twelve years, during which I focused on undergraduate teaching, outreach, and mathematical scholarship. In 2017, I shifted my professional focus toward a research-oriented career.
Although I now lead an active research group, I remain deeply committed to undergraduate teaching, curriculum development at all levels, and outreach to high-school students and teachers.
Upcoming Talks
Selected Recent Past Talks
University of Belgrade (Belgrade, Serbia)
International Conference on Nonlinearity, Nonlocality and Ultrametricity
(On the Occasion of Branko Dragovich's 80th Birthday)
Date: May 30, 2025
Title: Brownian Motion in the p-Adic Integers is a Limit of Discrete Time Random Walks
University of California, San Diego
Probability Seminar
Date: May 30, 2024
Title: p-Adic Brownian Motion is a Scaling Limit
University of California, Santa Barbara
Applied/PDE/DS Seminar
Date: May 24, 2024
Title: p-Adic Brownian Motion is a Scaling Limit
University of California, Riverside
MPDS Seminar
Date: May 2, 2024
Title: Any Brownian motion in a finite dimensional vector space over a local field is a scaling limit
Pace University (New York City, New York)
Metro New York Annual MAA Meeting
Date: April 29, 2023
Title: Discrete approximation of p-adic Brownian motion
Steklov Mathematical Institute of Russian Academy of Sciences (Moscow, Russia - Online)
International conference dedicated to the 100th anniversary of the birthday of V.S.Vladimirov
Date: January, 2023
Title: Components and exit times of Brownian motion in two or more p-adic dimensions
American Mathematics Society (Denver, Colorado)
Joint Mathematics Meeting, Special Session
Date: January, 2020
Title: p-Adic Brownian motion as a limit of discrete time random walks
Publications
Research Articles in Preparation
Note: I have other projects in preparation, but these are closest to completion and will be submitted within 6 months.
Cohen, A., Kissee, D., Weisbart, D.: Path integrals for discrete approximations of $p$-adic Brownian motion.
ArXiv Link: In preparation
Cohen, A., Weisbart, D.: Finite approximation of quantum systems.
ArXiv Link: In preparation
Kissee, D., Weisbart, D.: Banach spaces of distributions and the classification of elementary particles.
ArXiv Link: In preparation
Research Articles Completed at UCR
Note: Articles that are marked with an asterix (*) are education articles.
Stine, A., Weisbart, D.: A compositional framework for open kinematical systems in classical mechanics.
ArXiv Link: (To be posted shortly)
Rajkumar, R., Weisbart, D.: Scaling limits of random walks in 2-dimensional p-adic vector spaces and their component processes.
ArXiv Link: (To be posted shortly)
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).
ArXiv Link: http://arxiv.org/abs/2407.05561
Journal Link: https://rdcu.be/exfsO
*Wilbur, R., Atit, K., Agrawal, P., Lussier, C., Carrillo, B., Noack, D., Poon, Y., Weisbart, D.: Examining the role of spatial and mathematical processes and gender in postsecondary precalculus. Journal of Numerical Cognition. (2024). https://doi.org/10.23668/psycharchives.15476
Pierce, T., Rajkumar, R., Stine, A., Weisbart, D., Yassine, A.M.: Brownian motion in a vector space over a local field is a scaling limit. Expositiones Mathematicae. 42. (2024).
ArXiv Link: https://doi.org/10.48550/arXiv.2405.02502
Journal Link: https://doi.org/10.1016/j.exmath.2024.125607
Weisbart, D.: p-Adic Brownian motion is a scaling limit. Journal of Physics A: Mathematical and Theoretical. (2024). https://10.1088/1751-8121/ad40df
Abelgas, A., Carrillo, B., Palacios, J., Weisbart, D., Yassine, A.M.: Buffon’s problem determines Gaussian curvature in three geometries. Journal of Applied Probability. 61. 1-12, (2024). https://doi.org/10.1017/jpr.2023.114
*McMurran, M., Weisbart, D., Atit, K.: The relationship between students' gender and their confidence in the correctness of their solutions to complex and difficult mathematics problems. Learning and Individual Differences, Volume 107, (2023). https://doi.org/10.1016/j.lindif.2023.102349
Rajkumar, R., Weisbart, D.: Components and exit times of Brownian motion in two or more p-adic dimensions. J Fourier Anal Appl 29, 75 (2023). https://doi.org/10.1007/s00041-023-10053-z
Weisbart, D., Yassine, A.M.: Constructing span categories from categories without pullbacks. Pacific Journal of Mathematics 321, no. 2 (2023). https://doi.org/10.2140/pjm.2022.321.443
Weisbart, D.: Estimates of certain exit probabilities for p-adic Brownian bridges. Journal of Theoretical Probability 35, no. 3 (2022). https://doi.org/10.1007/s10959-021-01099-0
Weisbart, D.: On infinitesimal generators and Feynman–Kac integrals of adelic diffusion. Journal of Mathematical Physics 62, no. 10 (2021). https://doi.org/10.1063/5.0056119
Baez, J.C., Weisbart, D., Yassine, A.M.: Open systems in classical mechanics. Journal of Mathematical Physics 62, no. 4 (2021). https://doi.org/10.1063/5.0029885
Weisbart, D.: Modernizing Archimedes construction of π. Mathematics 8, no. 12 (2020). https://doi.org/10.3390/math8122204
Bakken, E., Weisbart, D.: p-Adic Brownian motion as a limit of discrete time random walks. Communications in Mathematical Physics 369, no. 2 (July 1, 2019): 371–402. https://doi.org/10.1007/s00220-019-03447-y
Bakken, E., Weisbart, D.: Continuous time p-adic random walks and their path integrals. Journal of Theoretical Probability 32, no. 2 (2019). https://doi.org/10.1007/s10959-018-0831-3
Taylor, D., Varadarajan, V.S., Virtanen, J., Weisbart, D.: Temperedness of measures defined by polynomial equations over local fields. Pacific Journal of Mathematics 296, no. 1 (May 1, 2018): 227–256. https://doi.org/10.2140/pjm.2018.296.227
Bakken, E.M., Digernes, T., Weisbart, D.: Brownian motion and finite approximations of quantum systems over local fields. Reviews in Mathematical Physics 29, no. 05 (June 2017): 1750016. https://doi.org/10.1142/S0129055X17500167
Prior to my position at UCR
Virtanen, J., Weisbart, D.: Elementary particles on p-adic spacetime and temperedness of invariant measures. P-Adic Numbers, Ultrametric Analysis, and Applications 6, no. 4 (October 1, 2014): 318–332. https://doi.org/10.1134/S2070046614040074
Bakken, E.M., Digernes, T., Lund, M.U., Weisbart, D.: Finite approximations of physical models over p-adic fields. P-Adic Numbers, Ultrametric Analysis, and Applications 5, no. 4 (October 1, 2013): 249–259. https://doi.org/10.1134/S2070046613040018
Digernes, T., Weisbart, D.: Matrix-valued Schrödinger operators over local fields. P-Adic Numbers, Ultrametric Analysis, and Applications 1, no. 2 (June 1, 2009): 136–144. https://doi.org/10.1134/S2070046609020058
Fernandez, R.N., Varadarajan, V.S., Weisbart, D.: Airy functions over local fields. Lett Math Phys 88, 187–206 (2009). https://doi.org/10.1007/s11005-009-0311-x
Digernes, T., Varadarajan, V.S., Weisbart, D.: Schrödinger operators on local fields: Self-adjointness and path integral representations for propagators. Infinite Dimensional Analysis, Quantum Probability and Related Topics 11, no. 04 (December 2008): 495–512. https://doi.org/10.1142/S0219025708003294
Varadarajan, V.S., Weisbart, D.: Convergence of quantum systems on grids. Journal of Mathematical Analysis and Applications 336, no. 1 (December 1, 2007): 608–624. https://doi.org/10.1016/j.jmaa.2007.02.073