# Noga Alon

## Tel Aviv University and IAS, Princeton

- Institute for Advanced Study
- Math Building Seminar Room (M101)
- Princeton, NJ
- Monday, November 25, 1996 at 11:15 am - 12:15 pm

## Randomness and Pseudo-Randomness in Discrete Mathematics

The discovery, demonstrated in the early work of Erdos, Shannon and
others, that deterministic statements can be proved by probabilistic
reasoning, led already in the first half of the century to several
striking results in Analysis, Number Theory, Combinatorics and
Information Theory. It soon became clear that the method, which is now
called the probabilistic method, is a very powerful tool for proving
results in Discrete Mathematics.
Most probabilistic proofs are existence, non-constructive arguments.
The rapid development of theoretical Computer Science, and its tight
connection to Combinatorics, stimulated the study of the algorithmic
aspects of these proofs.

The application of probabilistic techniques for proving deterministic
theorems, and the application of deterministic theorems for
derandomizing probabilistic existence proofs, form an interesting
combination of mathematical ideas from various areas, whose intensive
study in recent years led to the development of fascinating
techniques. I will survey some of these developments and describe
several related open problems.

dimacs-www@dimacs.rutgers.edu
Document last modified on October 28, 1996