Pacific Northwest Probability Seminar

  • Date: 10/24/2015
Balint Virag, University of Toronto (Birnbaum Lecturer)

University of Washington

The Birnbaum Lecture in Probability will be delivered by Balint Virag (University of Toronto) in 2015.

Northwest Probability Seminars are mini-conferences held at the University of Washington and/or Microsoft Research 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 2015 consists of Omer Angel (U British Columbia), Chris Burdzy (U Washington), Zhenqing Chen (U Washington), Yevgeniy Kovchegov (Oregon State U), David Levin (U Oregon), Yuval Peres (Microsoft) and David Wilson (Microsoft).
  • 10:00 Coffee Savery 166
  • 11:10 - 11:50 Mathav Murugan, University of British Columbia

Anomalous random walks with heavy-tailed jumps
Sub-Gaussian estimates for the nearest neighbor random walk are typical of fractal-like graphs. In this talk, I will describe a threshold behavior of heavy-tailed random walks on such graphs. This behavior generalizes the classical threshold corresponding to the second moment condition. This talk is based on joint work with Laurent Saloff-Coste.

  • 12:00 - 12:40 Zhenan Wang, University of Washington

Stochastic De Giorgi Iteration
We will start on the classical De Giorgi iteration for parabolic PDEs. We will explain how a stochastic version of De Giorgi iteration can be developed and applied to prove H\"older continuity for solution of stochastic partial differential equations with measurable coefficient. We will also introduce fine properties for the solutions obtained by applying the stochastic De Giorgi iterations.

  • 12:45 - 2:15 Lunch, catered, location, probability demos and open problems
  • 2:20 - 3:15 Balint Virag, University of Toronto

"Birnbaum Lecture"

  • 3:25 - 4:05 Juan M. Restrepo, Oregon State University

Taking Uncertainties into Account in Geosciences, Physics, and Engineering
Accounting for uncertainties has led us to alter our expectations of what is predictable and how such predictions compare to nature. A significant effort, in recent years, has been placed on creating new uncertainty quantification techniques, rediscovering old ones, and the appropriation of existing ones to account for uncertainties in modeling and simulations.

Is this nothing more than a greater reliance on statistics techniques in our regular business? Some of it is. However, as this presentation will recount and illustrate, there are important changes on how we perform the business of modeling and predicting natural phenomena: Bayesian inference is used to combine models and data (not just to compare models and data); sensitivity analyses and projection techniques influence mean-field modeling; data classification techniques allow us to work with the more general state variables, which subsume dynamic physical variables; we exploit complex stochastic representations to better capture multi-scale phenomena or to capture the small-scale correlations of big data sets.

In this expository talk I will summarize some of the pressing application issues and probabilistic methodologies, featuring along the way some of the work that my group has done in connection with nonlinear/non-Gaussian non-equilibrium problems.

  • 4:10 - 4:40 Coffee break Savery 260
  • 4:40 - 5:20 Yuval Peres, Microsoft Research

Random walk on the random graph
I will discuss the behavior of the random walk on two random graph models: on one hand the random regular graph with constant degree, and on the other hand the giant component of the supercritical Erdos-Renyi random graph with constant average degree. In the former case it is known that the walk mixes in logarithmic time and exhibits the cutoff phenomenon. In the latter case, while starting from the worst initial state delays mixing and precludes cutoff, it turns out that starting from a typical vertex induces the rapid mixing behavior of the regular case. (Joint work with Nathanael Berestycki, Eyal Lubetzky and Allan Sly.)


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