Since meeting the Wasserstein metric during my PhD journey, I knew about the 1998 paper “The Variational Formulation of the Fokker-Planck Equation” by Richard Jordan, David Kinderlehrer and Felix Otto, thinking this pioneering article lives in its own little corner of mathematics surrounded by Wasserstein-2 gradient flow enthusiasts. Few mathematicians I talked to outside of this bubble seemed to have ever heard of a JKO scheme. Little did I know that this gem is the single most downloaded article of the SIAM Journal on Mathematical Analysis since its 50 volumes of existence. Wow.
Why is it so popular? It describes the gradient flow structure of the Fokker-Planck equation using an implicit time discretization in the form of a sequence of variational problems, called “minimizing movements”. In doing so, it builds a bridge between geometric analysis, optimal transportation, quasistatic dissipative evolutions, applied partial differential equations and rational mechanics.
For a short summary of the paper and why so many people are interested in it, have a look at this recent article in SIAM NEWS by Felix Otto, mentioning at least 10 mathematicians I’ve had the chance to personally interact with.