Reading List

Books

Optimal Transport

• Santambrogio, Filippo. Optimal transport for applied mathematicians. Birkäuser, NY 55.58-63 (2015): 94. Download PDF
• Chewi, Sinho, Jonathan Niles-Weed, and Philippe Rigollet. Statistical optimal transport. Springer Nature, 2025. Download PDF

Gradient Flows

• Ambrosio, Luigi, Nicola Gigli, and Giuseppe Savaré. Gradient flows: in metric spaces and in the space of probability measures. Basel: Birkhäuser Basel, 2005. Download PDF
• Santambrogio, F. {Euclidean, metric, and Wasserstein} gradient flows: an overview. Bull. Math. Sci. 7, 87–154 (2017). Download PDF

Sampling

• Sinho Chewi, Log-Concave Sampling. (Unfinished Draft). Download PDF

Markov Semigroups and Functional Inequalities

• Bakry, D., Gentil, I., and Ledoux, M. Analysis and Geometry of Markov Diffusion Operators. Springer, 2014. Download PDF
• Chafaï, D. and Lehec, J. Logarithmic Sobolev Inequalities Essentials, lecture notes. Download PDF

Functional Analysis

• Bobrowski, Adam. Functional analysis for probability and stochastic processes: an introduction. Cambridge University Press, 2005. Download PDF
• Garling, David JH. Analysis on Polish spaces and an introduction to optimal transportation. Vol. 89. Cambridge University Press, 2018. Download PDF

Reproducing Kernel Hilbert Spaces

• Berlinet, A., & Thomas-Agnan, C. (2011). Reproducing kernel Hilbert spaces in probability and statistics. Springer Science & Business Media.

Stochastic Analysis

• Le Gall, Jean-François. Brownian motion, martingales, and stochastic calculus. Springer International Publishing Switzerland, 2016. Download PDF

Manifold

• Lee, John M. “Smooth manifolds.” Introduction to smooth manifolds. New York, NY: Springer New York, 2003. 1-29. Download PDF

Lie Algebra

• Carter R. Lie Algebras of Finite and Affine Type. Cambridge University Press; 2005. Download PDF

Economy & Finance

• Bernanke, Ben S. 21st century monetary policy: The Federal Reserve from the great inflation to COVID-19. WW Norton & Company, 2022. Download PDF
• Ormerod, P. (2007). Why most things fail: Evolution, extinction and economics. John Wiley & Sons. Download PDF

Papers

Sampling and Generative Modelling

• Chen, S., Chewi, S., Li, J., Li, Y., Salim, A., & Zhang, A. R. (2022). Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions. arXiv preprint arXiv:2209.11215. Download PDF

Mean-Field Langevin Dynamics

• Hu, Kaitong, et al. “Mean-field Langevin dynamics and energy landscape of neural networks.” Annales de l’Institut Henri Poincare (B) Probabilites et statistiques. Vol. 57. No. 4. Institut Henri Poincaré, 2021. Download PDF
• Chizat, Lénaïc. “Mean-field langevin dynamics: Exponential convergence and annealing.” arXiv preprint arXiv:2202.01009 (2022). Download PDF
• Kook, Y., Zhang, M. S., Chewi, S., Erdogdu, M. A., & Li, M. B. (2024, June). Sampling from the mean-field stationary distribution. In The thirty seventh annual conference on learning theory (pp. 3099-3136). PMLR. Download PDF
• Chen, F., Ren, Z., & Wang, S. (2025, November). Uniform-in-time propagation of chaos for mean field Langevin dynamics. In Annales de l’Institut Henri Poincare (B) Probabilites et statistiques (Vol. 61, No. 4, pp. 2357-2404). Institut Henri Poincaré. Download PDF
• Chewi, S., Nitanda, A., & Zhang, M. S. (2024). Uniform-in-$ N $ log-Sobolev inequality for the mean-field Langevin dynamics with convex energy. arXiv preprint arXiv:2409.10440. Download PDF Sildes

Optimization over the Space of Probability Measures

• Arbel, M., Korba, A., Salim, A., & Gretton, A. (2019). Maximum mean discrepancy gradient flow. Advances in neural information processing systems, 32. Download PDF
• Korba, A., Salim, A., Arbel, M., Luise, G., & Gretton, A. (2020). A non-asymptotic analysis for Stein variational gradient descent. Advances in Neural Information Processing Systems, 33, 4672-4682. Download PDF
• Zhu, J. J. (2024). Inclusive KL minimization: A Wasserstein-Fisher-Rao gradient flow perspective. arXiv preprint arXiv:2411.00214. Download PDF
• Zhu, J. J., & Mielke, A. (2022). Approximation, Kernelization, and Entropy-Dissipation of Gradient Flows: from Wasserstein to Fisher-Rao. Download PDF
• Xu, Y., & Li, Q. (2026). Random Coordinate Descent on the Wasserstein Space of Probability Measures. arXiv preprint arXiv:2604.01606. Download PDF

The cover image of this article was taken in Saipan, Commonwealth of the Northern Mariana Islands (U.S.).