I do research in mathematical probability.
A central theme is the study of large finite random structures,
obtaining asymptotic behavior as the size tends to infinity
via consideration of some suitable infinite random structure.
The topics are listed on the left; here is a guided tour.
I was most recently working with graduate student Lisha Li
on a model of partially observed networks.
And I have a curious model of
Coalescing random partitions of the plane.
I also enjoy little research projects arising from data gathered for my "Probability in the Real World" course
-- here is one on
game theory and one on queueing theory
and one on topological graph theory
and one on Elo ratings and the sports model.
My previous (2011-14) research focus has been
on Scale-invariant random spatial networks
and on FMIE processes,
the latter with former
During 2012-14 I worked with post-doc
Over 2007-10 I was focussing on
discrete spatial networks
flows through random networks,
partly with my recent student
Shankar Bhamidi. Various results remain to be written up.
During 2005-08 I was involved with two very different projects. First,
Combinatorial optimization over random data
and its scaling exponents with post-doc Charles Bordenave and Marc Lelarge.
And finally appearing in 2011 is the third and final paper in
stochastic models for phylogenetic trees
with former student Lea Popovic
and former post-doc Maxim Krikun.
During 2000-04 my main focus was on the overlapping topics of
and I remain interested in rigorous formalizations of the cavity method from
Also a series of papers with Gregory Miermont and Jim Pitman on
Nonuniform random mappings, ICRTs and Levy-type
which partially continue my 1990s work on the
continuum random tree.
Where are the papers?
Follow this link to a list (reverse chronological) of research and survey papers and to
electronic versions of papers since 1997.
slides from seminar and conference talks.
Here is a small list of
Simulations and pictures