The Eleventh Northwest Probability Seminar
October 24, 2009
Supported by the Mathematical Sciences
Research Institute (MSRI),
Pacific Institute for the Mathematical
Sciences (PIMS)
and Microsoft Research.
Speaker photographs
The Birnbaum
Lecture in Probability
will be delivered by
Persi Diaconis
(Stanford University) in 2009.
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.
The Scientific Committee for the NW Probability Seminar 2009
consists of Omer Angel (U British Columbia), Chris Burdzy (U Washington),
Zhenqing Chen (U Washington),
Yevgeniy Kovchegov (Oregon State U),
David Levin (U Oregon) and
Yuval Peres (Microsoft).
The talks will take place in Savery Hall 260.
Savery 264 is also reserved for the conference participants
(extra meeting room, extra whiteboards, etc.)
See the map
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 only after noon.
See
parking
fees
and
general
parking information.
Schedule
 10:40 Coffee Savery 264
 11:10 Robert Masson, University of British Columbia
Exponential tail bounds for looperased random walk in Z^2
Consider a simple random walk in Z^2 started at the origin and stopped at its first exit of the ball of radius n, and let M_n be the number of steps of its looperasure. Kenyon showed that E[M_n] is logarithmically asymptotic to n^{5/4}. In this talk, we give tail bounds on M_n. We establish exponential moments for M_n and thereby show that there exists c > 0
such that for all n and a>1, P(M_n > a E[M_n]) < 2exp(ca). Using a
second moment result for the looperasure of a specific conditioned random walk and an iteration argument, we also get the following bound on the lower tail: for all b < 4/5, there exist C and c'>0 such that for all n and a >1, P(M_n < a^{1} E[M_n]) < C exp(c a^b). Time permitting, we will discuss applications of this result to volume estimates for the uniform spanning tree in Z^2.
Joint work with Martin Barlow.
 12:00  1:15 Lunch, catered, HUB 108.
 1:15 Persi Diaconis, Stanford University
"Birnbaum Lecture": Graph Limits and Threshold Graphs
What does it mean for a sequence of graphs (random or not) to converge or for
one graph to be a good approximation to another? This is the subject of graph limits as
developed by Lovasz and many coauthors. It turns our that many of the basic results were
anticipated by the multivariate versions of deFinetti's theorem
(AldousHooverKallenberg). I will explain both sides of this subject and illustrate with
random threshold graphs. All of this is joint work with Susan Holmes and Svante Janson.
 2:15 Coffee break Savery 264
 2:30 Christopher Sinclair, University of Oregon
Pfaffian Point Processes and Random Matrices
An ensemble of matrices is a set of matrices together with a probability measure. The probability measure induces a point process on the space of eigenvalues of the set of matrices. The point process is called determinantal or Pfaffian if the joint intensities of the point process can be represented as determinants or Pfaffians of certain matrices associated with the ensemble. In this talk, I will give example of some ensembles which induce Pfaffian point processes and show how this structure allows many basic probabilistic quantities to be computed (e.g. the probability that a matrix has no eigenvalues in a given set, and the distribution for the absolute value of the largest eigenvalue). New ensembles and applications will be discussed within this framework.
 3:20 David Aldous, U.C. Berkeley and Microsoft Research

Spatial random networks
I will give an overview of ongoing research concerning networks linking
random vertices in twodimensional space, emphasizing two aspects.
(1) If we get to choose where to put edges, subject to a given total
length, then how efficient can we make the network in the sense of
providing routes whose length is not much larger than straightline
distance?
(2) There is a general class of "proximity graphs", defined for arbitrary
vertices, which are always connected. Applying to random points gives a
class of random networks which are connected and have bounded mean degree.
This class has scarcely been studied, but seems an appealing modeling
alternative to the classical geometric random graphs for which one cannot
have both connectivity and bounded mean degree.
 4:10  4:50 Problem session

Chair: Yuval Peres (Microsoft Research)
 6:00 Nohost dinner.
 Restaurant: Chiang's Gourmet.
7845 Lake City Way NE,
Seattle, WA 98115,
Tel: (206) 5278888
 Google directions with map
 Google directions with closeup map of restaurant neighborhood
 Google street view looking from Lake City Way  you cannot enter the restaurant
from Lake City Way
 Google street view looking from NE 80th St. Turn left from Lake City Way into NE 80th St
and then turn left into the restaurant parking lot.
 Google photo of the restaurant looking from Lake City Way
 Google photo of the restaurant looking from NE 80th St
