My recent work on a direct p-adic analogue of the Wiener process is currently under review. The law for the Wiener process and the Laplacian (the associated infinitesimal generator) are both radially symmetric. It is well known that the multidimensional Wiener process decomposes as a Cartesian product of stochastically independent one-dimensional Wiener processes. We show that the process respecting the analogous symmetries in p-adic vector spaces fails to have this property. Moreoever, we contrast exit time statistics with a process that does not obey the same symmetries and exhibits qualitatively different behavior.

Select Talks

  • 48th Annual New York State Regional Graduate Mathematics Conference
    • “Elements and Applications of p-Adic Analysis” (Slides) (April 1,2023)
  • JMM 2023 AMS Contributed Paper Session on Probability Theory and Stochastic Processes
    • “Components and Exit Times of Brownian Motion in Multiple p-Adic Dimensions” (Slides) (January 6, 2023)
  • JMM 2023 AMS Special Session on Advances in Markov Models: Gambler’s Ruin, Duality and Queueing Applications
    • “Components and Exit Times of Brownian Motion in Multiple p-Adic Dimensions” (Extended Slides) (January 7, 2023)
    • Professor Alan Krinik (Cal Poly Pomona) kindly invited me give an extended version of my contributed talk
  • Virtual Research Seminar on Non-Archimedean Analysis and Mathematical Physics (UT RGV)
    • “Diffusion Experiments in a p-Adic Universe” (September 21, 2022)