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Aldous's Brownian excursions, critical random graphs and the multiplicative coalescent.

David Clancy, UW Math
Monday, October 5, 2020 - 2:30pm to 3:30pm
Online. Please contact Prof. Soumik Pal for the link.
In the first installment of the Hidden Gems sequence, we're looking at the connection between Erdős–Rényi random graphs in a critical window and a Brownian motion with parabolic drift. We'll discuss how Aldous encodes the Erdős–Rényi graph with a discrete random walk, and discuss what are some consequences of this particular encoding. We will finish up by mentioning some subsequent results related to this model and/or Aldous's connection to Brownian motion with parabolic drift.
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