Sharp Convergence of Wasserstein Gradient Flows for Spectrally Nonnegative Interaction Energies

Zhengjiang Lin, Philippe Rigollet

We study the long-time behavior of Wasserstein gradient flows for interaction energies \[ \mathsf E[μ] = \frac12\iint_{M\times M}K(x,y)\,\mathrm dμ(x)\,\mathrm dμ(y) \] on a closed…