Pacific Northwest Probability Seminar
The Twenty Third Northwest Probability Seminar
November 4, 2023
Supported by the
University of Oregon,
Pacific Institute for the Mathematical
Sciences (PIMS), Baidu,
University of Washington
(Friends of Mathematics Fund),
and Milliman Fund.
Lecture in Probability
will be delivered by
(University of Pennsylvania) in 2023.
Northwest Probability Seminars are
mini-conferences held at the University of Washington
and organized in collaboration with
the Oregon State University, the University of British Columbia and
the University of Oregon.
There is no registration fee.
The Scientific Committee for the NW Probability Seminar 2023
consists of Omer Angel (U British Columbia), Chris Burdzy (U Washington),
Zhenqing Chen (U Washington), David Levin (U Oregon) and
Axel Saenz Rodríguez (Oregon State U).
near the University of Washington.
The talks will take place in Mary Gates Hall 241
(see the map).
Parking on UW campus is free on Saturdays only after noon.
- 10:00 - 11:00 Coffee Mary Gates Commons
- 11:00 - 11:50 Stefan Steinerberger, University of Washington
Particle Growth Models in the Plane (DLA, DBM, ...)
We'll discuss growth patterns in the plane. The most famous
such model is DLA where new particles arrive via a Brownian motion
and get stuck once they hit an existing particle: it forms the most beautiful
fractal patterns (pictures will be provided). Despite this, DLA is actually fairly
poorly understood and we will quickly survey the existing ideas (many of
which are due to Harry Kesten). I will then present a new type of growth
model that behaves similarly (many more pictures will be shown) and which
can be very precisely analyzed (in certain cases). No prior knowledge is
necessary, I'll explain everything from first principles.
- 12:00 - 12:50 Nick Marshall, Oregon State University
Random High-Dimensional Binary Vectors, Kernel Methods, and Hyperdimensional Computing
This talk explores the mathematics underlying hyperdimensional computing (HDC),
a computing paradigm that employs high-dimensional binary vectors. In HDC, data
is encoded by shifting and combining random high-dimensional binary vectors
in various ways. We study the problem of determining the optimal distribution
of random high-dimensional binary vectors for use in this construction.
- 1:00 - 3:00 Lunch, catered,
Mary Gates Commons
- 3:00 - 3:50 Robin Pemantle, University of Pennsylvania
"Birnbaum Lecture": Negative association and related properties
Negative dependence properties of random variables have
been valuable in proving limit theorems and tail bounds
often substituting when independence fails. I will begin
by reviewing the theory and uses of negative dependence
concepts for binary random variables, beginning with origins
in mathematical statistics and statistical mechanics.
Among the many concepts and definitions that have been
proposed, two stand out: negative association (NA) and the
strong Rayleigh property (SR). The former is a negative
dependence property that is sometimes hard to prove but
is very useful when it holds. The somewhat mysterious
Strong Rayleigh property implies negative dependence and
can in fact be a route to proving negative dependence.
The endpoint of this talk is to explore the limits of SA
by looking at cases where NA holds or is expected
to hold but SR does not. While this kills the hope
of proving NA for these models by establishing SR, it
also helps us see what allows NA to hold without SR,
which I hope will motivate and enable development of
new technology for proving NA.
- 4:00 - 4:30 Coffee Mary Gates Commons
- 4:30 - 5:20 Lucas Teyssier, University of British Columbia
On the universality of fluctuations for the cover time
How long does it take for a random walk to cover all the
vertices of a graph? And what is the structure of the uncovered set (the
set of points not yet visited by the walk) close to the cover time? We
show that on vertex-transitive graphs of bounded degree, this set is
decorrelated (it is close to a product measure) if and only if a simple
geometric condition on the diameter of the graph holds. In this case,
the cover time has universal fluctuations: properly scaled, the cover
time converges to a Gumbel distribution. To prove this result we rely on
recent breakthroughs in geometric group theory which give a quantitative
form of Gromov's theorem on groups of polynomial growth. We also prove
refined quantitative estimates showing that the hitting time of any set
of vertices is (irrespective of its geometry) approximately an
exponential random variable.
This talk is based on joint work with Nathanaël Berestycki and Jonathan
- 6:00 No-host (likely subsidized) dinner.
Mamma Melina. There will be set menu,
the first menu on this
The cost per person will be 36 dollars (this does not include tax and gratuity)
although it is likely that the conference will have funds to partly subsidize dinner.
Please bring cash. There will be a vegetarian option.
Wine and coffee can be ordered and paid for individually (cash only; alcohol will not be subsidized).
Address: 5101 25th Ave NE, Seattle, WA 98105.
See Google map.
The restaurant is a 20 minute walk
from Mary Gates Hall.