Northwest Probability Seminar 2014

This is a recap of the 16th Northwest Probability Seminar, a one-day mini-conference organized by the University of Washington, the Oregon State University, the University of British Columbia, the University of Oregon, and the Theory Group at Microsoft Research. In 2014, the conference was hosted at Microsoft, supported by Microsoft Research and the Pacific Institute for the Mathematical Sciences (PIMS).

The Birnbaum Lecture in Probability was given by Srinivasa Varadhan (New York University). [Past Birnbaum speakers]  Other speakers were Ioana Dumitriu (University of Washington), Alexander Holroyd (Microsoft Research), Tim Hulshof (University of British Columbia), and Benjamin Young (University of Oregon).

Talk titles and abstracts with links to video recordings

Alexander E Holroyd (Microsoft Research)

Title: Finitely dependent coloring

Abstract: Do local constraints demand global coordination? I’ll address a particularly simple formulation of this question: can the vertices of a graph be assigned random colours in a stationary way, so that neighboring colours always differ, but without long-range dependence? The quest to answer this has led to the discovery of a beautiful yet mysterious new stochastic process that seemingly has no right to exist, while overturning the conventional thinking on a fundamental 49-year old question.
(Joint work with Tom Liggett.)

Bio: Senior Researcher at Microsoft Research, Redmond. PhD: University of Cambridge (2000). Previous positions: UCLA (1999-2002), UC Berkeley (2002-2003), University of British Columbia (2002-2008). Awards: Rollo Davidson Prize (2004), Andre-Aisenstadt Prize (2007).

Tim Hulshof (University of British Columbia)

Title: Sharp higher order corrections for the critical value of a bootstrap percolation model

Abstract: Bootstrap Percolation (BP) models are simple cellular automata with a deterministic growth rule and random initial configuration. It is known that (critical) BP models on the lattice undergo a metastable phase transition on a lattice of fixed size, as the density of the initial configuration increases. Holroyd (2004) determined sharp first order asymptotics for the critical value for the canonical nearest-neighbor model in 2D. Surprisingly, this value turned out to be very far removed from computer simulations of BP on large lattices, suggesting that higher order corrections to the critical value may dominate even on large lattices. We study the scaling of the critical value for the so-called anisotropic (1,2)-model. Duminil-Copin and van Enter recently showed sharp first order asymptotics for the critical value of this model. We determine sharp second and third order corrections, and show that they are both large enough to dominate the critical value of anisotropic bootstrap percolation on any scale that is feasibly accessed by computers.
Based on joint work with Hugo Duminil-Copin, Aernout van Enter, and Robert Morris.

Bio: Tim Hulshof received his doctoral degree in 2013 under the supervision of Remco van der Hofstad at the Eindhoven University of Technology, the Netherlands. Currently he is a postdoctoral fellow at UBC and PIMS in Vancouver.

Srinivasa Varadhan (New York University)

Title: The role of compactness in large deviations

Abstract: The estimates obtained in large deviations are basically local estimates. While it is not a problem for lower bounds it is a problem for upper bounds. In the absence of exponential tightness some type of “compactification” of the space is needed. We will look at some examples.

Bio: Professor of Mathematics at Courant Institute New York University. Doctoral degree from Indian Statistical Institute (1963), postdoc at Courant Institute (63-66) followed by faculty position there. Member National Academy of Sciences in USA and Fellow of the Royal Society in UK. Awards include Steele Prize of AMS, Birkhoff prize of SIAM-AMS, and the Abel Prize of the Norwegian Academy of Sciences.

Benjamin Young (University of Oregon)

Title: Sampling from the Fomin-Kirillov distribution

Abstract: I will describe recent joint work with Sara Billey (UW) and Alexander Holroyd (MSR), generalizing earlier work of mine, in which we bijectively prove the general case of Macdonald’s identity in Schubert calculus. As a consequence, we also get a sampling algorithm for a probability distribution on reduced words which is implicit in work of Fomin and Kirillov. The proof involves several novel uses of David Little’s generalized “bumping” algorithm.

Bio: BY received his PhD under Jim Bryan and Richard Kenyon at UBC in 2008. After postdocs at McGill, MSRI, KTH and MSRI again, he became assistant professor at the University of Oregon in 2012. He works in combinatorics, particularly in areas which are close to algebraic geometry, probability, representation theory and statistical mechanics.

Ioana Dumitriu (University of Washington)

Title: A Regular Stochastic Block Model

Abstract: The famous Stochastic Block Model (SBM) has been recently completely solved independently by Massoulie and Mossel-Neeman-Sly. Inspired by their work, we have decided to examine a regular variant of the graph; the restrictive nature of the constraints makes the problem easier, but at the same time more challenging (given that we can push the thresholds lower, how much lower can we push them?) This is joint work with Gerandy Brito, Shirshendu Ganguly, Chris Hoffman, and Linh Tran.

Bio: Ioana is an Associate Professor in the Math Department at University of Washington. She received her PhD at MIT in 2003, working with Alan Edelman; after that, she was a Miller Fellow at UC Berkeley until 2006, before happily landing in the Great Pacific NW. She is the proud collector of mathematical labels, all of which are great, and none of which quite fits: “numerical analyst,” “combinatorialist,” “linear algebrist,” to which she is now very glad to add “probabilist.”