# Introduction to random graph models and some percolation results

Speaker: Sanjay Kumar Jhawar

Date: 19th March, 2019

Time: 9:15pm-10:15pm

Abstract: This discussion consists of introduction to some random graph models. The models are bond & site percolation model on $\mathbb{Z}^d$, Erdos- Reyni model, nearest neighbor model, Boolean model, random connection model (RCM), enhanced random connection model (eRCM), inhomogeneous eRCM (IeRCM) on Poisson point process of intensity $\lambda$. We define some events on these models and that will helps us to study the percolation behaviors. In the end we state some results on non-trivial phase transition and non-percolation at criticality for the model eRCM. The Russo-Seymour-Welsh (RSW) lemma is a key ingredient for the proof of the results.

Prerequisite: Basic Probability Theory.