Northwest Probability Seminars

The talks will take place in Thomson Hall 125. See the map of north-central 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 shift-coupled; 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 non-random function of Pi. The key ingredient is a translation-invariant 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
  • Self-normalized Cramer-Type 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\'er-type large deviation result for the standardized partial sums. In this paper we show that a Cram\'er-type large deviation theorem holds for self-normalized 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 $d_{n,\delta} = (\sum_{i=1}^n EX_i^2)^{1/2}/(\sum_{i=1}^n E|X_i|^{2+\delta})^{1/(2+\delta)}$ 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) 527-5247. See the map.. For reservation, please contact Zhen-Qing Chen (zchen@math.washington.edu ) at University of Washington.