The 2013 Porcelli Lectures speaker is Professor S.R. Srinivasa Varadhan of the Courant Institute for Mathematical Sciences at NYU.
- What is Large Deviations?
- Wednesday, April 17, 2013, 4:40–5:20
In probability theory, we often have to estimate the probabilities of various events. If they are not too small, we can try to approximate them. But sometimes they are very small and it can be important to know exactly how small they are. For example, in calculating conditional probabilities that are ratios, the conditioning event can have small probability. We are then looking at ratios of two small numbers, which may or may not be small.
- Scaling limits of large systems
- Thursday, April 18, 2013, 4:30–5:20
Often we have a large system whose behavior is specified through local interactions. We may be interested in understanding their large scale consequences. We will examine some examples of this.
- Counting graphs
- Friday, April 19, 2013, 4:30–5:20
Probability theory can be used to estimate, for large $N$, the number of graphs with $N$ vertices that have specified properties. For example, for a finite collection of finite graphs $\Gamma_j$, the ratio of the number of times $\Gamma_j$ occurs in the graph to the number of times it can occur in a complete graph can be specified.