Probability Day at UBC

A mathematical discipline in its own right, probability theory also plays an important role in many other areas of mathematics, such as partial differential equations, analysis, and combinatorics. It provides the theoretical basis for statistics. Probability is also an applied science, with important applications in statistical mechanics, mathematical biology, finance, theoretical computer science and telecommunications.

Hosted at PIMS by UBC's Probability group, this one day seminar series will feature lectures provided by noted probabilists.

Schedule:

11:00 -12:00 Gordon Slade (UBC)

Critical exponents for O(n) models.

Abstract : TBC 

12:00 - 1:30 Lunch break

1:30 - 2:30 Daniel Ahlberg (IMPA and Uppsala University)

Sharpness of the phase transition for continuum percolation on R^2

Many complex systems involving a large number of independent variables have come to be very well understood. One such example is Bernoulli percolation on a planar lattice. However, how to adapt the techniques to closely related models, such as continuum percolation in $\mathbb{R}^2$, may be far from obvious. We will describe some techniques of this kind that recently has been developed for Poisson Boolean percolation. We will focus on a certain two-stage construction that allows for a reduction to the discrete setting, where a larger arsenal of techniques is available for the study of phenomena such as sharp thresholds and noise sensitivity. Joint work with Vincent Tassion and Augusto Teixeira. 

2:30 - 3:00 Coffee Break, PIMS Lounge: ESB 4133

3:00 - 4:00 Asaf Nachmias (Tel Aviv University)

Slightly subcritical hypercube percolation

We will present some recent results about bond percolation on the hypercube {0,1}^m in the "slightly" subcritical phase, that is, just below the critical percolation scaling window. We estimate the size, diameter and mixing time of the largest components. A difficulty that arises only in the subcritical phase is that the cluster of the largest size does not attain the largest possible diameter. Therefore, we are able to analyze rather accurately the cluster of largest diameter, but not the cluster of largest size, leaving some interesting open problems. Joint work with Tim Hulshof.