Math

Research Interests

Stationary random measures, point processes, point-shifts, random walks, probability, measure theory.

Publications

  1. J. Murphy, Coupling and Unimodularity in Stationary Settings, Ph.D. Thesis (2019)
  2. F. Baccelli, M.-O. Haji-Mirsadeghi, and J. Murphy, Doeblin Trees, Electronic Journal of Probability (2019)
  3. J. Murphy, Exact Coupling of Random Walks on Polish Groups, Journal of Theoretical Probability (2018)
  4. J. Murphy, Point-shifts of Point Processes on Topological Groups, (preprint)
  5. J. Murphy, Resolving the one-dimensional autonomous flow-free explosion problem, SIAM Undergrad. Res. Online (2014)
  6. J. Murphy, Resolving the one-dimensional autonomous flow-free explosion problem, Carnegie Mellon University (2014)

Talks Given

  1. J. Murphy, Doeblin Trees, University of Texas (2019)
  2. J. Murphy, Markov Eternal Family Trees, University of Texas (2017)
  3. J. Murphy, Propp and Wilson Coupling from the Past, University of Texas (2017)
    • Reference: S. Foss and R. Tweedie, Perfect simulation and backward coupling

  4. J. Murphy, Exact Coupling of Random Walks on Polish Groups, University of Texas (2017)
  5. J. Murphy, On the Liouville Property of Stationary Random Graphs, University of Texas (2017)
  6. L. Ly, J. Murphy, and M. Stolarski, Threshold Dynamics with Applications to Image Processing, University of Texas (2016)
  7. J. Murphy, An Introduction to Stationary Random Measures on Topological Groups with Focus on Point-shift Foliations, University of Texas (2016)
  8. J. Murphy, An Elementary Proof of Rademacher's Theorem, University of Texas (2015)
  9. J. Murphy, A Brief Introduction to Processes of Flats, University of Texas (2015)
  10. J. Murphy, Existence for the Dirichlet Problem in Zaremba Domains, University of Texas (2015)
  11. J. Murphy, Arrow's Theorem by Boolean Fourier Analysis, University of Texas (2015)