About me
I am an associate professor in Industrial Engineering and Operations Research (IEOR) at Columbia University, affiliated with the Data Science Institute. From 20152017 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 in part by the NSF CAREER award DMS2045328.
Office: Mudd 306
Email: daniel.lacker (at) columbia (dot) edu
Lecture Notes
Publications and Preprints

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 logconcavity
With Sumit Mukherjee and Lane Chun Yeung. To appear in International Mathematics Research Notices. [arXiv]

Sharp uniformintime propagation of chaos
With Luc Le Flem. Probability Theory and Related Fields. [arXiv, DOI]

A labelstate 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]

Closedloop convergence for mean field games with common noise
With Luc Le Flem. To appear in 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 transportationinformation inequalities for Markov processes in terms of dimensionfree concentration
With Lane Chun Yeung. Annales de l’Institut Henri Poincaré. [arXiv, DOI]

Marginal dynamics of interacting diffusions on unimodular GaltonWatson 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 McKeanVlasov 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]

Manyplayer 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]

Nonexponential 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 closedloop Nash equilibria to the mean field game limit
Annals of Applied Probability. [arXiv, DOI]

On a strong form of propagation of chaos for McKeanVlasov 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 nagent 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 McKeanVlasov dynamics
SIAM Journal on Control and Optimization. [arXiv, DOI]

A nonexponential 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: November, 2023.