Research Interests

    Random walks on graphs, random walks in random environments, interacting particle systems, diffusions, heat kernel estimates.

 

Ph.D Thesis

    Adapted metrics and random walks on graphs. PDF cIRcle

 

Papers

  1. M. Folz. Volume growth and spectra of general graph Laplacians. To appear in Math. Z. arXiv:1204.4770 MZ version
  2. M. Folz. Volume growth and stochastic completeness of graphs. To appear in Trans. Amer. Math. Soc. arXiv:1201.5908 TAMS version
  3. M. Folz. Gaussian upper bounds for heat kernels of continuous time simple random walks. Elec. J. Prob. 16 (2011), 1693-1722. arXiv:1102.2265 EJP version
 

Presentations

  1. Brownian motion and random walks on graphs. UCLA Probability Seminar, May 2013.
  2. Volume growth and stochastic completeness of graphs. UBC Probability Seminar, September 2012.
  3. Volume growth and the spectrum of infinite graphs. Simon Fraser University Discrete Mathematics Seminar, July 2012.
  4. Volume growth and random walks on graphs. PIMS-mprime Summer School in Probability, June 2012.
  5. Video
  6. Gaussian upper bounds for heat kernels of continuous time random walks. UBC Probability Seminar, November 2011.
  7. Gaussian upper bounds for heat kernels of continuous time random walks on graphs. Cornell Probability Summer School, July 2010.
  8. Gaussian upper bounds for heat kernels on graphs and on manifolds. UBC Probability Graduate Student Seminar, May 2010.