About me

I am an associate professor in Industrial Engineering and Operations Research (IEOR) at Columbia University, affiliated with the Data Science Institute. From 2015-2017 I was an NSF postdoctoral fellow in Applied Mathematics at Brown University, and before that I completed my Ph.D. in 2015 at Princeton University in the department of Operations Research and Financial Engineering (ORFE). A major focus of my research is the theory and applications of mean field games, where the areas of interacting particle systems, stochastic control, and game theory intersect. Click here for a CV.

My research is supported by an Alfred P. Sloan Fellowship and the NSF CAREER award DMS-2045328.

Office: Mudd 306
Email: daniel.lacker (at) columbia (dot) edu

Lecture Notes

• Notes from my mini-course at the 2018 IPAM Graduate Summer School on Mean Field Games and Applications, titled "Probabilistic compactification methods for stochastic optimal control and mean field games."
• Rough lecture notes from the Spring 2018 PhD course (IEOR E8100) on mean field games and interacting diffusion models.

Publications and Preprints

• Convergence of coordinate ascent variational inference for log-concave measures via optimal transport
  With Manuel Arnese. Preprint. [arXiv]
• Independent projections of diffusions: Gradient flows for variational inference and optimal mean field approximations
  Preprint. [arXiv]
• Projected Langevin dynamics and a gradient flow for entropic optimal transport
  With Giovanni Conforti and Soumik Pal. Preprint. [arXiv]
• Approximately optimal distributed stochastic controls beyond the mean field setting
  With Joe Jackson. Preprint. [arXiv]
• Mean field approximations via log-concavity
  With Sumit Mukherjee and Lane Chun Yeung. International Mathematics Research Notices. [arXiv, DOI]
• Sharp uniform-in-time propagation of chaos
  With Luc Le Flem. Probability Theory and Related Fields. [arXiv, DOI]
• A label-state formulation of stochastic graphon games and approximate equilibria on large networks
  With Agathe Soret. Mathematics of Operations Research. [arXiv, DOI]
• Stationary solutions and local equations for interacting diffusions on regular trees
  With Jiacheng Zhang. Electronic Journal of Probability. [arXiv, DOI]
• Closed-loop convergence for mean field games with common noise
  With Luc Le Flem. Annals of Applied Probability. [arXiv, DOI]
• Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions
  Probability and Mathematical Physics. [arXiv, DOI]
• Quantitative approximate independence for continuous mean field Gibbs measures
  Electronic Journal of Probability. [arXiv, DOI]
• A characterization of transportation-information inequalities for Markov processes in terms of dimension-free concentration
  With Lane Chun Yeung. Annales de l’Institut Henri Poincaré. [arXiv, DOI]
• Marginal dynamics of interacting diffusions on unimodular Galton-Watson trees
  With Kavita Ramanan and Ruoyu Wu. Probability Theory and Related Fields. [arXiv, DOI]
• Local weak convergence for sparse networks of interacting processes
  With Kavita Ramanan and Ruoyu Wu. Annals of Applied Probability. [arXiv, DOI]
• A case study on stochastic games on large graphs in mean field and sparse regimes
  With Agathe Soret. Mathematics of Operations Research. [arXiv, DOI]
• Denseness of adapted processes among causal couplings
  With Mathias Beiglböck. Preprint. [arXiv]
• Superposition and mimicking theorems for conditional McKean-Vlasov equations
  With Mykhaylo Shkolnikov and Jiacheng Zhang. Journal of the European Mathematical Society. [arXiv, DOI]
• Locally interacting diffusions as Markov random fields on path space
  With Kavita Ramanan and Ruoyu Wu. Stochastic Processes and their Applications. [arXiv, DOI]
• Many-player games of optimal consumption and investment under relative performance criteria
  With Agathe Soret. Mathematics and Financial Economics. [arXiv, DOI]
• Inverting the Markovian projection, with an application to local stochastic volatility models
  With Mykhaylo Shkolnikov and Jiacheng Zhang. Annals of Probability. [arXiv, DOI]
• Non-exponential Sanov and Schilder theorems on Wiener space: BSDEs, Schrödinger problems and control
  With Julio Backhoff Veraguas and Ludovic Tangpi. Annals of Applied Probability. [arXiv, DOI]
• On the convergence of closed-loop Nash equilibria to the mean field game limit
  Annals of Applied Probability. [arXiv, DOI]
• On a strong form of propagation of chaos for McKean-Vlasov equations
  Electronic Communications in Probability. [arXiv, DOI]
• From the master equation to mean field game limit theory: Large deviations and concentration of measure
  With François Delarue and Kavita Ramanan. Annals of Probability. [arXiv, DOI]
• From the master equation to mean field game limit theory: A central limit theorem
  With François Delarue and Kavita Ramanan. Electronic Journal of Probability. [arXiv, DOI]
• Mean field and n-agent games for optimal investment under relative performance criteria
  With Thaleia Zariphopoulou. Mathematical Finance. [arXiv, DOI]
• Rare Nash equilibria and the price of anarchy in large static games
  With Kavita Ramanan. Mathematics of Operations Research. [arXiv, DOI]
• Limit theory for controlled McKean-Vlasov dynamics
  SIAM Journal on Control and Optimization. [arXiv, DOI]
• A non-exponential extension of Sanov's theorem via convex duality
  Advances in Applied Probability. [arXiv,DOI]
• Mean field games of timing and models for bank runs
  With René Carmona and François Delarue. Applied Mathematics & Optimization. [arXiv, DOI]
• Liquidity, risk measures, and concentration of measure
  Mathematics of Operations Research. [arXiv, DOI]
• Law invariant risk measures and information divergences
  Dependence Modeling. [arXiv, DOI]
• Translation invariant mean field games with common noise
  With Kevin Webster. Electronic Communications in Probability. [arXiv, DOI]
• A general characterization of the mean field limit for stochastic differential games
  Probability Theory and Related Fields. [arXiv, DOI]
  Winner of the 2014 SIAG/FME Conference Paper Prize.
• Mean field games with common noise
  With René Carmona and François Delarue. Annals of Probability. [arXiv, DOI] Errata: [PDF, DOI]
• Mean field games via controlled martingale problems: Existence of Markovian equilibria
  Stochastic Processes and their Applications. [arXiv, DOI]
• A probabilistic weak formulation of mean field games and applications
  With René Carmona. Annals of Applied Probability. [arXiv, DOI]
• Stochastic differential mean field game theory
  My PhD Thesis. [PDF]

Last updated: April, 2024.