I realized this week that my former PhD advisor has spent a significant amount of his research time juggling with the Talagrand γ2 and the Bakry-Émery Γ2. He belongs to this very small set of individuals versed in these two universes, between analysis, geometry, and probability. The link is clearly the Gaussian law. It might be amusing to connect the two in a deep statement.
Recently, a kind of Bakry-Émery Γ2 was developed for Markov chains on metric spaces.
More recently, the Talagrand γ2 was used successfully for random walks on graphs.
Leave a Comment