Northwest Probability Seminars
NW Probability Seminar 2003
October 18, 2003
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 Thomson Hall 125.
See the map
of northcentral campus.
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.
Conference schedule (click on names to see photos)
 11:00 Alexander E. Holroyd ,
University of British Columbia.

Extra Heads and Stable Marriage
Let Pi be a Poisson point process on R^d, and let Pi^* be the same process
with an added point at the origin. Thorisson proved that Pi and Pi^* can
be shiftcoupled; that is, one may choose a random point Y of Pi such that
the process viewed from Y is equal in law to Pi^*.
We prove that such a Y may be chosen to be a nonrandom function of Pi.
The key ingredient is a translationinvariant rule for allocating sets of
equal volume (forming a partition of R^d) to the points of Pi. See
http://www.math.ubc.ca/~holroyd/stable.html for a picture. Such a rule
may be constructed using a celebrated algorithm of Gale and Shapley for
producing stable marriages.
We also consider how large the random variable Y must be. The answer
depends strikingly on the dimension. In 2 dimensions Y must have
infinite mean, while in 3 dimensions it may have exponential tails.
 12:00 Yuval Peres , UC Berkeley
and Microsoft Research.

Zeros of the i.i.d. Gaussian power series:
a determinantal process with conformally invariant dynamics
Consider the zero set of a random power series with i.i.d.
complex Gaussian coefficients. We show that these zeros form a
determinental process: more precisely, their joint intensity can be
written as a minor of the Bergman kernel. The repulsion between zeros can
be studied via a dynamic version where the coefficients perform Brownian
motion; we show that this dynamics is conformally invariant.
(Talk based on joint work with Balint Virag, Toronto).
 1:00  2:30 Lunch Break
 2:45 Qiman Shao,
University of Oregon

Selfnormalized CramerType Large Deviations
for Independent Random Variables
Let $X_1, X_2, \cdots $ be independent random variables with
zero means and finite variances.
It is well known that
a finite exponential
moment assumption is necessary for a Cram\'ertype large deviation
result for the standardized partial sums.
In this paper we show that a Cram\'ertype large
deviation theorem holds for selfnormalized sums only under
a finite $(2+\delta)$th moment $(0< \delta \leq 1)$. In particular,
we have $P(S_n /V_n \geq x)=
%%\sum_{i=1}^n X_i \geq x (\sum_{i=1}^n X_i^2)^{1/2})
(1\Phi(x)) \Big(1+O(1) (1+x)^{2+\delta} /d_{n,\delta}^{2+\delta}\Big)$
for $0 \leq x \leq d_{n,\delta}$,
where $d_{n,\delta} = (\sum_{i=1}^n EX_i^2)^{1/2}/(\sum_{i=1}^n
EX_i^{2+\delta})^{1/(2+\delta)}$ and $V_n= (\sum_{i=1}^n X_i^2)^{1/2}$.
Recent developments and related problems will also be discussed.
 3:45 Jiangang Ying,
Fudan University and University of Washington.

On Regular Subspaces of H^1([0, 1])
In this talk, we shall indicate that there exist regular Dirichlet
subspaces of H^1([0, 1]), which corresponds to reflected Brownian motion
on the unit interval [0, 1]. We characterize all of its
regular subspaces by the scale functions of the associated diffusions.
It is proved that the associated diffusion is obtained from the reflected
Brownian by a time change and a state space transformation.
 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.