Tsinghua University Pao-Lu Hsu Distinguished Lecture


Student No.: 50

 Time: 16:30-17:30pm, May 14 (Tue.), May 16 (Thu.)

Instructor: S.R.Srinivasa Varadhan  [Courant Institute of Mathematical Sciences]

Place: Lecture Hall, Floor 3, Jin Chun Yuan West Building

Starting Date: 2013-5-14

Ending Date: 2013-5-16

 Lecture 1

Title: Scaling Limits, Large Deviations and Particle Systems.

Time: 16:30-17:30pm, May 14 (Tue.)

Tea break: 16:00-16:30pm

Abstract: Large systems are often studied by rescaling. The limiting behavior of the rescaled system is usually simpler. The theory of large deviations which estimates the probabilities of rare events is useful in studying the collective behavior of a large system of particles and their scaling limits. We will examine some examples.



Lecture 2

Title: Large Deviations and Random Graphs.

Time: 16:30-17:30pm, May 16 (Thu.)

Tea break: 16:00-16:30pm

Abstract: We consider a random graph with $N$ vertices where each edge, independently of others, has probability $p$ of being there. We can calculate easily the expected number of triangles and other subgraphs with a finite number of vertices. We examine the large deviation theory for the number of such objects and illustrate its use with some applications.