This is an informal study group covering topics in probability. Speakers volunteer to present recent papers on topics selected by the group at large. Grad students, postdocs, and faculty are all encouraged to attend.

We are in the midst of a digital revolution that is driving the development and deployment of new kinds of sensing systems with ever-increasing delity and resolution. To address the logistical and computational challenges involved in dealing with such high-dimensional data, we often depend on compression, which aims at finding the most concise representation of a signal that is able to achieve a target level of acceptable distortion. One of the most popular techniques for signal compression is known as transform coding, and typically relies on fi nding a basis or frame that provides compressible representations for signals in a class of interest. By a compressible representation, we mean that the signal is well-approximated by a signal with only K nonzero coe cients. Leveraging the concept of transform coding, compressive sensing (CS) has emerged as a new framework for signal acquisition and sensor design. CS enables a potentially large reduction in the sampling and computation costs for sensing signals that have a sparse or compressible representation.

- · Monday, Feb. 08, 2010: Liouville Property, Amenability, Discrete Fractals and Automaton Groups (Gidi Amir)
- · Monday, Feb. 22, 2010: Scaling Exponents for Directed Polymers in 1+1 Dimensions, Part III (Tom Alberts)
- · Monday, Mar. 01, 2010: Scaling exponents for directed polymers in dimension 1+1, part III (Tom Alberts)
- · Monday, Apr. 26, 2010: More details of Jeff Schenker's proof of eigenvector localization for band matrices (Ben Rifkind)
- · Monday, May. 10, 2010: The Doob h-transform: theory and examples (Alex Bloemendal)
- · Monday, May. 17, 2010: Doob's h-transform: a few more examples (Alex Bloemendal)
- · Monday, Oct. 04, 2010: Sample Path Properties of Stochastic Flows (Dima Dolgopyat)
- · Monday, Oct. 18, 2010: Sample Path Properties of Stochastic Flows, Part II (Dima Dolgopyat)
- · Monday, Oct. 25, 2010: Sample Path Properties of Stochastic Flows, Part III (Dima Dolgopyat)
- · Friday, Jul. 29, 2011: SLE in multiply connected domains (Gregory F. Lawler)
- · Friday, Dec. 02, 2011: A model of migration under constraints (Raoul Normand)
- · Friday, Jan. 20, 2012: Local Limit Theorem for Random Walks on Free Groups (Andrew Stewart)
- · Friday, Feb. 03, 2012: The Law of the Iterated Logarithm (Eric Hart)
- · Friday, Mar. 16, 2012: Random matrices: Getting inside the bulk! (Van Vu)
- · Friday, Mar. 30, 2012: A Brief Introduction to Compressed Sensing (Kai Yang)
- · Friday, Apr. 13, 2012: The Minimum Cost of a Random Assignment (Mustazee Rahman)
- · Tuesday, May. 01, 2012: An Introduction to the Dirichlet Process (Tom Alberts)