|09:00 to 09:50||Joel Tropp (California Institute of Technology, California, US)||
Random products and quantum simulation
How does a product of random matrices behave? This question has a long history in dynamical systems and ergodic theory, where the focus is on asymptotic behavior as the number of factors increases. It has also been studied within high-dimensional statistics and free probability, where the focus is on the asymptotic behavior as the dimension increases. Recently, products of random matrices have received renewed attention as a model for the behavior of randomized optimization algorithms, where it is important to obtain results for a fixed number of factors with a fixed dimension.
This talk outlines an easy method for obtaining such nonasymptotic concentration inequalities for a product of random matrices. As an application, we will show how this approach allows us to design an optimal randomized algorithm for the simulation of a quantum system. No background in random matrix theory or quantum information will be required.
The results are drawn from two collaborations: http://arxiv.org/abs/2003.05437 <http://arxiv.org/abs/2003.05437>, with De Huang, Jonathan Niles-Weed, and Rachel Ward. http://arxiv.org/abs/2008.11751 <http://arxiv.org/abs/2008.11751>, with Chi-Fang (Anthony) Chen, Hsin-Yuan (Robert) Huang, and Richard Kueng.
|17:30 to 18:20||Rahul Roy (Indian Statistical Institute, Delhi, India)||
A non-planar random graph and its planar scaling limit
We study the two dimensional version of a random graph introduced by Athreya, et al (2008). This random graph, also called the torchlight model is a non-planar directed random graph. We show that the scaling limit of this graph is the Brownian Web.
This is joint work with Azadeh Parvaneh.
|18:30 to 19:20||Anette Hosoi (Massachusetts Institute of Technology, Cambridge, US)||
Short Stories of Probability and Sports
In light of recent advances in data collection, sports possess a number of features that make them an ideal testing ground for new analyses and algorithms. In this talk I will describe a few studies that lie at the intersection of sports and data. The first centers on fantasy sports which have experienced a surge in popularity in the past decade. One of the consequences of this recent rapid growth is increased scrutiny surrounding the legal aspects of the games, which typically hinge on the relative roles of skill and chance in the outcome of a competition. While there are many ethical and legal arguments that enter into the debate, the answer to the skill versus chance question is grounded in mathematics. In this talk I will analyze data from daily fantasy competitions and propose a new metric to quantify the relative roles of skill and chance in games and other activities. Time permitting, in the second part of this talk, I will briefly outline two additional studies that lie at the intersection on sports and probability. The first is a collaboration with Major League Baseball to determine the physics behind the recent increase in the rate of home runs; in particular I will enumerate different potential drivers for the observed increase and evaluate the evidence in the data (box score, ball tracking, weather, etc) in support of each theory. The second explores one aspect of the impact of the pandemic on sports through data associated with opening NFL stadiums to fans.
|19:30 to 20:20||Nike Sun (Massachusetts Institute of Technology, Cambridge, US)||
Phase transitions in random constraint satisfaction problems.
I will survey recent progress in determination of asymptotic behavior for random constraint satisfaction problems, including phase transitions and some understanding of solution geometry. I will discuss (as time permits) two ideas that played an important role in these works: (1) combinatorial models for the solution geometry, and (2) contractivity of tree recursions as a tool for calculating expected partition functions on sparse random graphs. This lecture is based in part on joint works with Zsolt Bartha, Jian Ding, Allan Sly, and Yumeng Zhang.