An introduction to the probabilistic method through the Lov\'asz Local Lemma
Combinatorics
2019-09-25 v1 Probability
Abstract
We illustrate the use of probability theory in existential proofs, focusing on the Lov\'asz 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.
Keywords
Cite
@article{arxiv.1909.11078,
title = {An introduction to the probabilistic method through the Lov\'asz Local Lemma},
author = {Irfan Alam},
journal= {arXiv preprint arXiv:1909.11078},
year = {2019}
}
Comments
11 pages; Originally written in 2015 as an expository paper for a course called "Communicating Mathematics II" at Louisiana State University