## Northwest Probability Seminar 2012

- Date: 10/13/2012

Microsoft Research

This is 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. This year the

conference is being hosted at Microsoft.

Talk abstracts

** 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.

**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.

**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.

**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.

**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.

09:45 - 11:15 Coffee and muffins

11:15 - 11:55 Asaf Nachmias

12:00 - 12:40 Douglas Rizzolo

12:45 - 01:45 Lunch (catered)

01:45 - 02:15 Probability demos

02:20 - 03:15 Birnbaum lecture -- Jeff Steif, expository lecture on noise sensitivity

03:25 - 04:05 Son Luu Nguyen

04:10 - 04:35 Tea and snacks

04:35 - 05:15 Geoffrey Grimmett

06:00 - Dinner (no-host, at Haiku sushi & seafood buffet, downtown Redmond)

There is no registration fee. Participants are requested to email David.Wilson@microsoft.com in advance so that adequate food may be arranged for. Breakfast, lunch, and coffee will be free.

The talks will take place in Building 99 at Microsoft. Parking at Microsoft is free.

Please see the official webpage http://research.microsoft.com/en-us/events/nwprob2012/ for further information.