An introduction to the probabilistic method through the Lovász Local Lemma

Abstract

We illustrate the use of probability theory in existential proofs, focusing on the Lovász Local Lemma. This result gives a lower bound for the probability of avoiding a suitable finite collection of events. We describe some applications of this result in hypergraph packing and Latin transversals.

11 pages; Originally written in 2015 as an expository paper for a course called "Communicating Mathematics II" at Louisiana State University