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

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.