Author

Philippe Rigollet

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#machine learning Preprint Sep 2026

Sharp Convergence of Wasserstein Gradient Flows for Spectrally Nonnegative Interaction Energies

We study the long-time behavior of Wasserstein gradient flows for interaction energies \[ \mathsf E[\mu] = \frac12\iint_{M\times M}K(x,y)\,\mathrm d\mu(x)\,\mathrm d\mu(y) \] on a closed manifold $M$. For kernels diagonal in a Laplace eigenbasis with nonnegative spectral coefficients, we prove a differential inequality...

Zheng-Jiang Lin, Philippe Rigollet · 0 citations

Preprint Sep 2026

Quantitative Diffusive Limits for Singular Nonlocal Transport

We study the nonlocal continuity equation \[ \partial_t\mu_b =\operatorname{div}\!\left( \mu_b\nabla\log\bigl((I-b^2\Delta)^{-1}\mu_b\bigr) \right) \] on a closed connected Riemannian manifold. For smooth strictly positive initial data, we prove that as $b \to 0$, its global solution converges to heat flow $\mu(t)$ at...

Andrea Agazzi, Giuseppe Bruno, Federico Pasqualotto et al. · 0 citations