Northwest Probability Seminar

The talks will take place in SAV 249 (Savery Hall). See the map of north-central campus. The Savery Hall is marked with big bold white letters. So is the HUB (Student Union Building) where the lunch will be served.

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.

Tentative schedule

• 11:00 David C. Brydges, University of British Columbia.
  • Branched Polymers and Dimensional Reduction
    In 1981 Parisi and Sourlas conjectured exact critical exponents for Self-Avoiding Branched Polymers in $D=2,3$ dimensions. We (D. Brydges and J. Imbrie) prove that that the partition function for branched polymers equals the pressure of a hard core gas in two less dimensions with negative activity. The conjectures are a corollary.

• 12:00 Jim Fill, The Johns Hopkins University and Microsoft Research.
  • The Randomness Recycler: A new technique for perfect sampling
    For many probability distributions of interest, it is quite difficult to obtain samples efficiently. Often, Markov chains are employed to obtain approximately random samples from these distributions. The primary drawback to traditional Markov chain methods is that the mixing time of the chain is usually unknown, which makes it impossible to determine how close the output samples are to having the target distribution. Here we present a new protocol, the randomness recycler (RR), that overcomes this difficulty. Unlike classical Markov chain approaches, an RR-based algorithm creates samples drawn exactly from the desired distribution. Other perfect sampling methods such as coupling from the past use existing Markov chains, but RR does not use the traditional Markov chain at all. While by no means universally useful, RR does apply to a wide variety of problems. For several problem instances, it gives the first expected linear time interruptible algorithms for generating observations. I will discuss how RR applies to self-organizing lists, the Ising model, random independent sets, random colorings, the random cluster model, and other problems.
    (This talk will be based on joint work with Mark Huber of Duke University.)
    

• 1:00 - 2:30 catered lunch in room 200AB in the HUB (Student Union Building). See the map.

• 2:30 Christopher Hoffman, University of Washington.
  • Phase Transition in Dependent Percolation
    We will consider two models of dependent percolation and prove that they both exhibit a phase transition.

• 3:30 Enrique Thomann, Oregon State University.
  • Stochastic Cascades applied to the Navier Stokes Equations
    The Navier Stokes equations model the evolution of the state of an incompressible fluid and have served to motivate profound developments in many areas of modern applied mathematics including Harmonic Analysis, Scientific Computation and Partial Differential Equations. In this lecture, existence and regularity of solutions of these equations will be studied using a probabilistic representation of the Fourier transform of the solution as an expected value of a product functional of a branching random walk. To this effect, the notion of a majorizing kernel is introduced to obtain conditions under which the expected value is well defined, giving existence and uniqueness of solutions, while the regularity of the solution can also be ascertained from properties of these majorizing kernels. Connections of these results with the more classical work of Kato on mild solutions of the Navier Stokes equations and of McKean branching Brownian motion on the Kolmogorov-Petrovskii and Piskunov equations will be presented as well.
    This talk is based on joint work with R. Bhattacharya (Indiana University) and L. Chen, S. Dobson, R. Guenther, C. Orum, M. Ossiander and E. Waymire (Oregon State University)

• 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.
  This Indian restaurant has a large selection of food including seafood, lamb. They also have vegetarian dishes and salads.