Research
Research Interests: Probability theory; random maps, 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'm often found at the the probaility seminar or discrete math seminar.
Some co-authors:
Publications
(very not up to date; update coming soon.)- Localization for Linearly Edge
Reinforced Random Walks.
with Nicholas Crawford and Gady Kozma - Deterministic approximations of
random reflectors.
with Krzysztof Burdzy and Scott Sheffield - Avoidance Coupling.
with Alexander E. Holroyd, James Martin, David B. Wilson and Peter Winkler - A pattern theorem for random
sorting networks.
with Vadim Gorin and Alexander E. Holroyd - The Phase Transition for Dyadic
Tilings.
with Alexander E. Holroyd, Gady Kozma, Johan Wästlund and Peter Winkler - Rotor walks on general trees.
with Alexander E. Holroyd - Deterministic Thinning of Finite
Poisson Processes.
with Alexander E. Holroyd and Terry Soo - Random Subnetworks of Random
Sorting Networks.
with Alexander E. Holroyd - One-dimensional long-range
diffusion-limited aggregation I.
with Gideon Amir, Itai Benjamini and Gady Kozma - Scaling limit of the invasion
percolation cluster on a regular tree.
with Jesse Goodman and Mathieu Merle - Discrete low-discrepancy
sequences.
with Alexander E. Holroyd, James B. Martin, James Propp - Global divergence of spatial coalescents.
With Nathanael Berestycki and Vlada Limic.
- Stationary map coloring.
With Itai Benjamini, Ori Gurel-Gurevich, Tom Meyerovitch, and Ron Peled.
- Amenability of linear-activity
automaton groups.
With Gideon Amir and Balint Virag. - Sums and products along sparse
graphs.
With Noga Alon, Itai Benjamini and Eyal Lubetzky. - The TASEP speed
process.
With Gideon Amir and Benedek Valko. - The Non-Backtracking Spectrum
of the Universal Cover of a Graph.
With Joel Friedman and Shlomo Hoory. - 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. - The oriented swap process.
With Ander Holroyd and Dan Romik.
Ann. Probab., to appear, 2009. - Invasion percolation on regular
trees.
With Jesse Goodman, Frank den Hollander, and Gordon Slade.
Ann. Probab., 36(2):420--466, 2008. - Card shuffling and Diophantine
approximation.
With Yuval Peres and David Wilson.
Ann. Appl. Probab., 18(3):1215--1231, 2008. - Random sorting networks.
With Ander Holroyd, Dan Romik and Balint Virag.
Adv. in Math., 215(2):839--868, 2007. - Transience of percolation
clusters on wedges.
With Itai Benjamini, Noam Berger, and Yuval Peres.
Electron. J. Probab., 11:no. 25, 655--669, 2006. - The stationary measure of a
2-type totally asymmetric exclusion process.
J. Combin. Theory Ser. A, 113(4):625--635, 2006. - The jammed phase of the
Biham-Middleton-Levine traffic model.
With Ander Holroyd and James Martin.
Electron. Comm. Probab., 10:167--178, 2005. -
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. - Routing complexity of faulty
networks.
With Itai Benjamini, Eran Ofek, and Udi Wieder.
Random Structures Algorithms, 32(1):71--87, 2008. - A phase transition for the
metric distortion of percolation on the hypercube.
With Itai Benjamini.
Combinatorica, 27(6):645--658, 2007. - Random
walks that avoid their past convex hull.
With Itai Benjamini and Balint Virag.
Electron. Comm. Probab., 8:6--16, 2003. - Growth and percolation on
the uniform infinite planar triangulation.
Geom. Funct. Anal., 13(5):935--974, 2003. - Uniform infinite planar
triangulations.
With Oded Schramm.
Comm. Math. Phys., 241(2-3):191--213, 2003. - A
large Wiener sausage from crumbs.
With Itai Benjamini and Yuval Peres.
Electron. Comm. Probab., 5:67--71, 2000.