Research

Research Interests: Probability theory; percolation, random graphs, random walks, particle processes, scaling limits.

I am a member of the probability group at UBC. I'm also interested in discrete maths.

I am organizing a probability working group on graph limits.

My co-authors:


Publications

  1. Localization for Linearly Edge Reinforced Random Walks.
    with Nicholas Crawford and Gady Kozma
  2. Deterministic approximations of random reflectors.
    with Krzysztof Burdzy and Scott Sheffield
  3. Avoidance Coupling.
    with Alexander E. Holroyd, James Martin, David B. Wilson and Peter Winkler
  4. A pattern theorem for random sorting networks.
    with Vadim Gorin and Alexander E. Holroyd
  5. The Phase Transition for Dyadic Tilings.
    with Alexander E. Holroyd, Gady Kozma, Johan Wästlund and Peter Winkler
  6. Rotor walks on general trees.
    with Alexander E. Holroyd
  7. Deterministic Thinning of Finite Poisson Processes.
    with Alexander E. Holroyd and Terry Soo
  8. Random Subnetworks of Random Sorting Networks.
    with Alexander E. Holroyd
  9. One-dimensional long-range diffusion-limited aggregation I.
    with Gideon Amir, Itai Benjamini and Gady Kozma
  10. Scaling limit of the invasion percolation cluster on a regular tree.
    with Jesse Goodman and Mathieu Merle
  11. Discrete low-discrepancy sequences.
    with Alexander E. Holroyd, James B. Martin, James Propp
  12. Global divergence of spatial coalescents.
    With Nathanael Berestycki and Vlada Limic.
  13. Stationary map coloring.
    With Itai Benjamini, Ori Gurel-Gurevich, Tom Meyerovitch, and Ron Peled.
  14. Amenability of linear-activity automaton groups.
    With Gideon Amir and Balint Virag.
  15. Sums and products along sparse graphs.
    With Noga Alon, Itai Benjamini and Eyal Lubetzky.
  16. The TASEP speed process.
    With Gideon Amir and Benedek Valko.
  17. The Non-Backtracking Spectrum of the Universal Cover of a Graph.
    With Joel Friedman and Shlomo Hoory.
  18. A sharp threshold for minimum bounded-depth and bounded-diameter spanning trees and steiner trees in random networks.
    With Abraham Flaxman, and David Wilson.
    Combinatorica, to appear, 2009.
  19. The oriented swap process.
    With Ander Holroyd and Dan Romik.
    Ann. Probab., to appear, 2009.
  20. Invasion percolation on regular trees.
    With Jesse Goodman, Frank den Hollander, and Gordon Slade.
    Ann. Probab., 36(2):420--466, 2008.
  21. Card shuffling and Diophantine approximation.
    With Yuval Peres and David Wilson.
    Ann. Appl. Probab., 18(3):1215--1231, 2008.
  22. Random sorting networks.
    With Ander Holroyd, Dan Romik and Balint Virag.
    Adv. in Math., 215(2):839--868, 2007.
  23. Transience of percolation clusters on wedges.
    With Itai Benjamini, Noam Berger, and Yuval Peres.
    Electron. J. Probab., 11:no. 25, 655--669, 2006.
  24. The stationary measure of a 2-type totally asymmetric exclusion process.
    J. Combin. Theory Ser. A, 113(4):625--635, 2006.
  25. The jammed phase of the Biham-Middleton-Levine traffic model.
    With Ander Holroyd and James Martin.
    Electron. Comm. Probab., 10:167--178, 2005.
  26. Random infinite permutations and the cyclic time random walk.
    In Discrete random walks (Paris, 2003), Discrete Math. Theor. Comput. Sci. Proc., AC, pages 9--16. Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2003.
  27. Routing complexity of faulty networks.
    With Itai Benjamini, Eran Ofek, and Udi Wieder.
    Random Structures Algorithms, 32(1):71--87, 2008.
  28. A phase transition for the metric distortion of percolation on the hypercube.
    With Itai Benjamini.
    Combinatorica, 27(6):645--658, 2007.
  29. Random walks that avoid their past convex hull.
    With Itai Benjamini and Balint Virag.
    Electron. Comm. Probab., 8:6--16, 2003.
  30. Growth and percolation on the uniform infinite planar triangulation.
    Geom. Funct. Anal., 13(5):935--974, 2003.
  31. Uniform infinite planar triangulations.
    With Oded Schramm.
    Comm. Math. Phys., 241(2-3):191--213, 2003.
  32. A large Wiener sausage from crumbs.
    With Itai Benjamini and Yuval Peres.
    Electron. Comm. Probab., 5:67--71, 2000.