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Math Colloquium: Bootstrap Percolation on Uniform Attachment Graphs

Wednesday, November 14, 2018

3:00 PM-4:00 PM

Huseyin Acan, PhD, Drexel University

Abstract: Bootstrap percolation is a process defined on a graph, which starts with a set S of initially infected vertices. Afterward, at each step, an uninfected vertex with at least r infected neighbors becomes infected and stays infected forever. If r=1, then all vertices in a connected graph get infected at some point as long as there is at least one infected vertex initially. However, for r>1, the final set of infected vertices depends on the graph and S.

We study bootstrap percolation on a uniform attachment graph. This is a random graph on the vertex set {1,…,n}, where each vertex v makes k selections from {1,…,v-1} uniformly and independently, and these selections determine the edge set. We start the process with a random S. Our main interest is finding a threshold value of the size of S for the spread of infection to all vertices. I will talk about the upper and lower bounds we have on this threshold, which are not far from each other.

Joint work with Boris Pittel.

Contact Information

Georgi Medvedev
gsm29@drexel.edu

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Location

Papadakis Integrated Sciences Building, Room 108, 3245 Chestnut Street, Philadelphia, PA 19104

Audience

  • Everyone