**Emergence of a Giant Component in Heterogeneous Dual Random Intersection Graphs**

J. Tipan Verella

(MGIC)

**Abstract:**

Consider building a graph, ER_n (c), where n is the number of vertices, and 0<c<n is a constant, in the following manner. For each pair of vertices (i,j) we put an edge between them with probability p_n (c)=c/n. In 1960, Paul Erdös and Alfréd Rényi introduced this canonical random graph model and showed that for c<1, all the connected components of such a graph would be of order O("log" n) for n large, but that if c>1, the graph would contain a connected component of size O(n). In a statistical physics sense, the ER_n (c) graph undergoes a phase transition at c=1. In the ER_n (c) model, the edges are generated independently and they all have the same probability p_n (c). The heterogeneous dual random intersection graph model, G(V,W,p), is a random graph model in which both the homogeneity and the independence assumptions are dropped. We will show that G(V,W,p) undergo a similar phase transition.

**Biographical Sketch:**

Tipan Verella was born in Belgium (through no fault of his own), but thankfully raised in Haiti. He studied Mathematics at the University of Maryland at College Park, Applied and Computational Mathematics at Johns Hopkins University and Systems and Information Engineering at the University of Virginia. His research focused on latent structures of complex socio-behavioral systems, which he investigates using probability theory on discrete structures. He's career in Data Science started in 2004 in Baltimore Maryland when he worked for Advertising.com a pioneering AdTech company that was subsequently acquired by AOL. He is passionate about Haiti, inter-sectional social justice, and cultural heritage and how they are impacted by technology. He loves talking to Prof. Sameena Mulla (to whom he is married), discussing all things Haiti or Mathematics with his son Ibo, and keeping in touch with his various (2 brothers and 3 sisters) siblings. He lives in Milwaukee Wisconsin, where he works for MGIC as a Data Science Architect and helps organize Data Driven Wisconsin conference.

**Date and time: **

Saturday, April 24, 2021

12:45 PM—2:30 PM

**Zoom Meeting Link:**

https://umassboston.zoom.us/j/94937250908