### 14th Northwest Probability Seminar – Recurrence of planar graph limits.

#### Date

October 22, 2012

#### Speakers

Asaf Nachmias

#### Affiliation

University of British Columbia

Try Microsoft Edge A fast and secure browser that's designed for Windows 10 Get started

This is a recap of the 14th 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. 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 **Jeff Steif** (Chalmers University of Technology). [Past Birnbaum speakers]

Geoffrey Grimmett (Cambridge), Asaf Nachmias (UBC), Douglas Rizzolo (UW), and Son Luu Nguyen (OSU) also spoke.

9:45 – 11:15 | Coffee and muffins |

11:15 – 11:55 | Asaf Nachmias |

12:00 – 12:40 | Douglas Rizzolo |

12:45 – 1:45 | Lunch (catered) |

1:45 – 2:15 | Probability demos |

2:20 – 3:15 | Birnbaum lecture — Jeff Steif, expository lecture on noise sensitivity |

3:25 – 4:05 | Son Luu Nguyen |

4:10 – 4:35 | Tea and snacks |

4:35 – 5:15 | Geoffrey Grimmett |

6:00 – | Dinner (no-host, at Haiku sushi & seafood buffet, downtown Redmond) |

** Jeff Steif **(Chalmers University of Technology)

*Title:* Boolean Functions, Noise Sensitivity, Influences and Percolation

*Abstract:* Noise sensitivity concerns the phenomenon that certain types of events (Boolean functions) are sensitive to small noise. This topic is related to the notion of influence, which is a way to specify the importance of a particular variable on an event. These concepts become especially interesting in the context of percolation theory. Some important tools in this area are discrete Fourier analysis and randomized algorithms in theoretical computer science. In this lecture, I will give an overview of this subject.

*Bio:* JS received his PhD under Donald Ornstein at Stanford University in 1988. After postdocs at Rutgers and Cornell, he moved to Chalmers University in Gothenburg, Sweden where he became professor in 1998. Later, he was professor at Georgia Institute of technology but returned to Sweden. His interests are percolation, Markov random fields, interacting particle systems and ergodic theory.

** Asaf Nachmias **(University of British Columbia)

*Title:* Recurrence of planar graph limits

*Abstract:* We prove that any distributional limit of finite planar graphs in which the degree of the root has an exponential tail is almost surely recurrent. As a corollary, we obtain that the uniform infinite planar triangulation and quadrangulation (UIPT and UIPQ) are almost surely recurrent, resolving a conjecture of Angel, Benjamini and Schramm.

Joint work with Ori Gurel-Gurevich.

*Bio:* Asaf is an assistant professor at the University of British Columbia. Before joining UBC he was a postdoc at Microsoft Research and at MIT.

** Douglas Rizzolo **(University of Washington)

*Title:* Schroeder’s problems and random trees

*Abstract:* In 1870 Schroeder introduced four problems concerning the enumeration of bracketings of words or sets of a given size. We will consider what uniform draws from these bracketings look like as the size of the word or set goes to infinity. Connections will be made to the recently developed theory of Markov branching trees as well as several types of conditioned Galton-Watson trees.

Joint work with Jim Pitman.

*Bio:* Douglas Rizzolo is a Research Associate and NSF Postdoctoral Fellow at the University of Washington. He received his doctoral degree in mathematics from UC Berkeley in 2012 under the supervision of Jim Pitman.

** Son Luu Nguyen **(Oregon State University)

*Title:* Linear-Quadratic-Gaussian Mixed Game with Continuum-Parametrized Minor Players

*Abstract:* We consider a mean field linear-quadratic-Gaussian game with a major player and a large number of minor players parametrized by a continuum set. The mean field generated by the minor players is approximated by a random process depending only on the initial state and the Brownian motion of the major player, and this leads to two limiting optimal control problems with random coefficients, which are solved subject to a consistent requirement on the mean field approximation. The set of decentralized strategies constructed from the limiting control problems has an epsilon-Nash equilibrium property when applied to the large but finite population model.

Joint work with Minyi Huang.

*Bio:* Son Nguyen obtained his Ph.D. from Wayne State University, Detroit, Michigan, in July 2010. He finished his Ph.D. thesis with Professor George Yin. He was a research fellow at School of Mathematics & Statistics, Carleton University from September 2010 to August 2012. Currently, he is a research fellow at Mathematics Department, Oregon State University.

** Geoffrey Grimmett** (Cambridge University)

*Title:* The star-triangle transformation in probability theory

*Abstract:* The star-triangle transformation was `discovered’ in 1899. It has since become one of the basic tools for studying disordered systems in two dimensions, and it is known amongst physicists as the `Yang-Baxter equation’. We shall explain its harmony with de Bruijn’s theory of tilings and isoradial graphs, as developed by Kenyon and co-authors. Then we outline its use in proving universality for percolation in two dimensions.

*Bio:* GRG is Professor of Mathematical Statistics at Cambridge University. He is spending his sabbatical leave at Microsoft, where he hopes to continue and develop his collaborative activities.

October 22, 2012

Asaf Nachmias

University of British Columbia

October 22, 2012

Jeff Steif

Chalmers University of Technology

October 19, 2012

Douglas Rizzolo

October 19, 2012

Son Luu Nguyen

Oregon State University

October 19, 2012

Geoffrey Grimmett

Cambridge University