
Northwest Probability Seminar
LINK TO 2005 SEMINAR WEB PAGE
The Sixth Northwest Probability Seminar
October 23, 2004
The Birnbaum
Lecture in Probability will be delivered by Ofer Zeitouni (University
of Minnesota) in 2004.
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. There is no registration fee. Participants
are requested to contact Chris Burdzy
(burdzy@math.washington.edu
) in advance
so that adequate facilities may be arranged for.
The Scientific Committee for the NW Probability Seminar 2004
consists of Chris Burdzy (U Washington), Zhenqing Chen (U Washington),
Ed Perkins (U British Columbia), QiMan Shao (U Oregon) and Ed Waymire
(Oregon State U).
The talks will take place in Savery 239 and 241.
See the map
of northcentral campus for the location of Savery 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.
Schedule
 10:30 Coffee  Savery Hall 239/241
 11:00 Mina Ossiander, Oregon State University
(photo)

A Probabililistic Representation of Solutions
to Incompressible NavierStokes Equations
The NavierStokes equations governing the velocity of
incompressible fluids in 3 dimensions have been studied
extensively over the last century. Important open
questions still remain concerning the existence and
uniqueness of smooth solutions for given initial
velocity. The goal of this talk is to describe
a representation of solutions in physical space
as scaled expectations of functionals of a Markov
branching process. If the forcing and initial
data are jointly small enough in a certain function
space this representation can be used to show that
a weak solution to the NavierStokes equations
exists and is unique for all time.
 12:00 Rick Kenyon, University of British Columbia
(photo)

Asymptotics of random crystalline surfaces
We consider a natural family of models of random crystalline surfaces
in R^3 arising in the planar dimer model (domino tiling model).
For fixed boundary conditions,
the law of large numbers leads to a PDE for the limit
shape (when the lattice spacing tends to zero)
of the surfaces. This PDE is a variant of the
complex Burger's equation and can be "solved" analytically.
This is surprising since the surfaces generically have both
smooth parts and facets.
The interplay between analytic (even algebraic)
functions and facet formation in the surfaces leads to some
interesting questions in real algebraic geometry.
 1:00  2:30 Lunch  Student Union Building 209A ("HUB")
 2:45 Ofer Zeitouni,
University of Minnesota
(photo)

"Birnbaum Lecture": Results and challenges in the study of multidimensional random
walks in random environments
Random walks in random environments on Z^d
represent a perfect playground for
probabilists: there are many interesting phenomena, several
outstanding open problems, and recent progress. I will describe the model,
some predictions made about it, and some partial answers. For the closely
related problem of diffusions in random environments, I will describe
recent results (obtained with A.S. Sznitman) that prove diffusivity
in the perturbative regime for d\geq 3.
 3:45 Oded Schramm, Microsoft Research
(photo)

Sensitivity, complexity, harmonic analysis and exceptional times
of Boolean functions
Let $f:\{1,1\}^n\to\{1,1\}$ be a Boolean function on the discrete cube.
If $f$ is likely to change when a small collection of random bits
of its input are flipped, then we say that $f$ is noise sensitive.
The sensitivity of $f$ is easily read off from its Fourier expansion.
We describe results by several authors relating the Fourier expansion
to various measures of complexity of $f$.
Some interesting conclusions are:
(1) If $f$ is monotone, then any randomized algorithm
that determines $f$ has some bit that it examines with probability
at least $c n^{1/3}$. This is sharp, up to $\log n$ terms.
(2) A dynamic version of critical percolation on the triangular grid
in the plane has exceptional times in which the origin is in an
infinite cluster (but the exceptional times have measure zero).
 5:30 No host dinner at
Cedars Restaurant on Brooklyn.
Click on the restaurant name to go to its Web page.

