About me
I am an assistant 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). My research so far has focused largely on the theory and applications of mean field games, where the areas of interacting particle systems, stochastic control, and game theory intersect. More broadly, I am interested in many topics in probability and mathematical finance. Click here for a CV.
My research is supported in part by the Air Force Office of Scientific Research Grant FA95501910291 and the NSF CAREER award DMS2045328 (starting July 2021).
Office: Mudd 306
Email: daniel.lacker (at) columbia (dot) edu
Lecture Notes
Publications and Preprints

Stationary solutions and local equations for interacting diffusions on regular trees
With Jiacheng Zhang. Preprint. [arXiv]

Closedloop convergence for mean field games with common noise
With Luc Le Flem. Preprint. [arXiv]

Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions
Preprint. [arXiv]

Quantitative approximate independence for continuous mean field Gibbs measures
Preprint. [arXiv]

A characterization of transportationinformation inequalities for Markov processes in terms of dimensionfree concentration
With Lane Chun Yeung. Preprint. [arXiv]

Marginal dynamics of interacting diffusions on unimodular GaltonWatson trees
With Kavita Ramanan and Ruoyu Wu. Preprint. [arXiv]

Local weak convergence for sparse networks of interacting processes
With Kavita Ramanan and Ruoyu Wu. Preprint. [arXiv]

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 (major update of 2018 version). [arXiv]

Superposition and mimicking theorems for conditional McKeanVlasov equations
With Mykhaylo Shkolnikov and Jiacheng Zhang. Preprint. [arXiv]

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, 2021.