Student Probability Seminar

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Critical Erdos-Renyi Graph and Multiplicative Coalescence

Speaker: Zhenfeng Tu, NYU Courant

Location: Warren Weaver Hall 1314

Date: Monday, May 1, 2023, 3 p.m.

Synopsis:

Erdos-Renyi graph is a classical model for random graphs, which has applications in studying complex networks, percolation, and random matrix theory. A fundamental idea to study the limiting behavior of Erdos-Renyi graph is by looking at a random walk that fully characterizes the graph. By looking at the limit of the random walk, we prove that in the critical regime, the size of connected components converges weakly to the excursion length of some Brownian excursion, and the number of surplus edges converges to a point process with intensity given by the excursion. If time permits we will also look at how connected components merge as we increase the probability of connecting two vertices.