Northwest Probability Seminar
The Third NW Probability Seminar
October 20, 2001
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,
the University of Oregon, and the Theory Group at the Microsoft
Research. This annual Seminar is held on the second
to last Saturday of October of each year.
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 talks will take place in SAV 249 (Savery Hall).
See the map
of northcentral campus. The Savery Hall is marked
with big bold white letters. So is the HUB (Student
Union Building) where the lunch will be served.
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.
Tentative schedule
 11:00 David C. Brydges,
University of British Columbia.

Branched Polymers and Dimensional Reduction
In 1981 Parisi and Sourlas conjectured exact critical
exponents for SelfAvoiding Branched Polymers in $D=2,3$ dimensions.
We (D. Brydges and J. Imbrie) prove that that the partition function
for branched polymers equals the pressure of a hard core gas in two
less dimensions with negative activity. The conjectures are a
corollary.
 12:00 Jim Fill, The Johns Hopkins University
and Microsoft Research.

The Randomness Recycler: A new technique for perfect sampling
For many probability distributions of interest, it is quite difficult to
obtain samples efficiently. Often, Markov chains are employed to obtain
approximately random samples from these distributions. The primary
drawback to traditional Markov chain methods is that the mixing time of the
chain is usually unknown, which makes it impossible to determine how close
the output samples are to having the target distribution. Here we present
a new protocol, the randomness recycler (RR), that overcomes this
difficulty. Unlike classical Markov chain approaches, an RRbased
algorithm creates samples drawn exactly from the desired distribution.
Other perfect sampling methods such as coupling from the past use existing
Markov chains, but RR does not use the traditional Markov chain at all.
While by no means universally useful, RR does apply to a wide variety of
problems. For several problem instances, it gives the first expected
linear time interruptible algorithms for generating observations. I
will discuss how RR applies to selforganizing lists, the Ising
model, random independent sets, random colorings, the random cluster
model, and other problems.
(This talk will be based on joint work with Mark Huber of Duke University.)
 1:00  2:30 catered lunch in room 200AB in
the HUB (Student Union Building).
See the map.
 2:30 Christopher Hoffman,
University of Washington.

Phase Transition in Dependent Percolation
We will consider two models of dependent percolation and prove
that they both exhibit a phase transition.
 3:30 Enrique Thomann, Oregon State University.

Stochastic Cascades applied to the Navier Stokes Equations
The Navier Stokes equations model the evolution of the state of
an incompressible fluid and have served to motivate profound developments
in many areas of modern applied mathematics including Harmonic Analysis,
Scientific Computation and Partial Differential Equations.
In this lecture, existence and regularity of solutions of
these equations will be studied using a probabilistic representation of the
Fourier transform of the solution as an expected value of a product
functional of a branching random walk. To this effect,
the notion of a majorizing kernel
is introduced to obtain conditions under which the expected value
is well defined, giving existence and uniqueness of solutions,
while the regularity of the solution can also be ascertained
from properties of these majorizing kernels.
Connections of these results with the more classical
work of Kato on mild solutions of the Navier Stokes equations and
of McKean branching Brownian motion
on the KolmogorovPetrovskii and Piskunov equations
will be presented as well.
This talk is based on joint work with R. Bhattacharya (Indiana University)
and L. Chen, S. Dobson, R. Guenther, C. Orum, M. Ossiander and E. Waymire
(Oregon State University)
 5:30 No host dinner at Cedars Restaurant on Brooklyn
Address: 4759 Brooklyn NE, Seattle,
Tel. (206) 5275247. See the
map.
For reservation, please contact ZhenQing Chen
(zchen@math.washington.edu
) at University
of Washington.
This Indian restaurant has a large selection of food including
seafood, lamb. They also have
vegetarian dishes and salads.