
Northwest Probability Seminar
The Ninth Northwest Probability Seminar
October 20, 2007
The Birnbaum
Lecture in Probability will be delivered by Rich Bass
(University of Connecticut) this year.
Northwest Probability Seminars are oneday
miniconferences held at the University of Washington
and organized in collaboration with
the Oregon State University, the University of British Columbia,
University of Victoria,
the University of Oregon, and the Theory Group at the Microsoft
Research. There is no registration fee. Participants
are requested to contact ZhenQing Chen
(zchen@math.washington.edu
) in advance
so that adequate facilities may be arranged for.
The Scientific Committee for the NW Probability Seminar 2007
consists of Chris Burdzy (U Washington), Zhenqing Chen (U Washington),
Edwin Perkins (U British Columbia), David Levin (U Oregon)
and Yevgeniy Kovchegov (Oregon State U).
The talks will take place in Thomson Hall 125.
See the map
of northcentral campus for the location of
Thomson Hall and
Padelford Hall
(the Department of Mathematics is in the Padelford Hall).
More
campus maps are available at the UW Web site.
Parking on UW campus is free on Saturdays after 12:00 (noon).
More information is available at a
parking Web site
provided by UW.
This year, October 20, 2007 is also the Husky game day so the traffic
may be slow before and after the game.
Schedule
 10:00 Coffee and Registration  Thomson Hall 119
 11:00 David Levin,
University of Oregon

On Mixing of meanfield Glauber dynamics
Abstract: I will discuss the Glauber dynamics for the Ising model
on the complete graph on n vertices, reporting on joint work
with M. Luczak and Y. Peres. At high temperature,
we show that the dynamics exhibits a cutoff (in a window
of size order n) at the (wellknown) mixing time of
order n \log n. At the critical temperature, we prove the
mixing time is order n^{3/2}. Finally, if the dynamics are
restricted to states with nonnegative magnetization, at low temperature
the mixing time is order n\log n, contrasting with
exponential mixing time for the unrestricted dynamics.
 12:00 Anthony Quas,
University of Victoria

Distances in Positive Density Sets
Abstract: Given a set of distances D, one can consider the graph G_{d,D} on R^d where
two points are adjacent if they are separated by a distance belonging to D
and ask for its chromatic number. The case where D={1} is the
HadwigerNelson problem and it is known that 4<=chi(G_{2,{1}})<=7. If the
colour classes are required to be measurable, we obtain the measurable
chromatic number \chi_m(G_{d,D}). It is known that 5<=\chi_m(G_{2,{1}})<=7.
In the case where D is unbounded, it turns out that \chi_m(G_{d,D})=\infty.
We give a conceptual new proof of this and discuss possible extensions to
the general (nonmeasurable) case.
 1:00  2:30 Lunch
 2:30 David Wilson,
Microsoft Research

Boundary Partitions in Trees and Dimers
Abstract: Given a finite planar graph, a grove is a spanning forest in which
every component tree contains one or more of a specified set of
vertices (called nodes) on the outer face. For the uniform measure on
groves, we compute the probabilities of the different possible node
connections in a grove. These probabilities only depend on boundary
measurements of the graph and not on the actual graph structure, i.e.,
the probabilities can be expressed as functions of the pairwise
electrical resistances between the nodes, or equivalently, as
functions of the DirichlettoNeumann operator (or response matrix) on
the nodes. These formulae can be likened to generalizations (for
spanning forests) of Cardy's percolation crossing probabilities, and
generalize Kirchhoff's formula for the electrical resistance.
Remarkably, when appropriately normalized, the connection
probabilities are in fact integercoefficient polynomials in the
matrix entries, where the coefficients have a natural combinatorial
interpretation. A similar phenomenon holds in the socalled
doubledimer model: connection probabilities of boundary nodes are
polynomial functions of certain boundary measurements, and as formal
polynomials, they are specializations of the grove polynomials. Upon
taking scaling limits, we show that the doubledimer connection
probabilities coincide with those of the contour lines in the Gaussian
free field with certain natural boundary conditions. These results
have direct application to connection probabilities for
multiplestrand SLE_2, SLE_8, and SLE_4.
Joint work with Richard Kenyon.
 3:303:45 Coffee  Thomson Hall 119
 3:45 Rich Bass,
University of Connecticut

"Birnbaum Lecture": Random sampling and probability
Abstract: The ``random sampling'' in the title has nothing whatsoever to
do with statistics. Instead, it refers to the perfect reconstruction
of
a bandlimited function from samples, a classical problem of
Fourier analysis and signal processing. With deterministic sampling,
almost everything is known in one dimension and almost nothing
is known in higher dimensions. It turns out that one loses very
little in
efficiency by using random sampling, and in return one can use
probabilistic techniques to get some interesting theoretical
results.
This is joint work with Karlheinz Groechenig.
 5:30 No host dinner at
Cedars Restaurant on Brooklyn.
Click on the restaurant name to go to its Web page.
The Northwest Probability Seminar 2005.

