Currently, I am an Assistant Professor at Department of Industrial Engineering and Operations Research, Columbia University. Before joining Columbia IEOR, I was a postdoctoral researcher at Department of Industrial Engineering and Operations Research, UC Berkeley, and an assistant adjunct professor at Department of Mathematics, UCLA. I obtained my Ph.D. from Department of Statistics, UC Berkeley. My advisor was Jim Pitman . Before coming to Berkeley, I obtained an engineer diploma (Diplôme d'ingénieur) from Ecole Polytechnique, France.

My research interests are probability theory, machine learning, and financial technology. Some of my current research projects involve reinforcement learning with human feedback including diffusion alignment and direct preference optimization.

[46] Fine-tuning of diffusion models via stochastic control: entropy regularization and beyond .

Submitted.

[45] Score-based diffusion models via stochastic differential equations -- a technical tutorial .

with Hanyang Zhao. Submitted (growing out of the writeup).

[44] Contractive diffusion probabilistic models .

with Hanyang Zhao. Submitted. .

[43] Transaction fee mechanism for Proof-of-Stake protocol .

with David D. Yao. Submitted.

[42] Finite and infinite weighted exchangeable sequences .

Submitted.

[41] Exact Bayesian geostatistics using predictive stacking .

with Lu Zhang and Sudipto Banerjee. Submitted.

[40] The convergence rate of vanishing viscosity approximations for mean field games .

with Yuming Paul Zhang. Submitted.

[39] Policy iteration for the deterministic control problems -- a viscosity approach .

with Hung Vinh Tran and Yuming Paul Zhang. Submitted.

[38] Systemic robustness: a mean-field particle system approach .

with Erhan Bayraktar, Gaoyue Guo and Yuming Paul Zhang. Submitted.

[37] Stability of shares in the Proof of Stake protocol -- concentration and phase transitions .

Submitted.

[36] Learning an arbitrary mixture of two multinomial logits
.

Submitted.

[35] Discrete simulated annealing: a convergence analysis via the Eyring--Kramers law .

with Yuhang Wu and Xun Yu Zhou. To appear in * Numerical Algebra, Control and Optimization *.

[34] Polynomial voting rules .

with David D. Yao. To appear in * Mathematics of Operations Research. *

[33] Trading and wealth evolution in the Proof of Stake protocol .

* Proof-of-Stake for Blockchain Networks: Fundamentals, Challenges and Approaches (2024) Chapter 7, 135-161. *

[32] Fixed-domain asymptotics under Vecchia's approximation of spatial process likelihoods .

with Lu Zhang and Sudipto Banerjee. To appear in * Statistica Sinica. *

[31] McKean-Vlasov equations involving hitting times: blow-ups and global solvability
.

with Erhan Bayraktar, Gaoyue Guo and Yuming Paul Zhang. * Annals of Applied Probability (2024) vol.34, no.1B, 1600–1622. *

[30] Escaping saddle points efficiently with occupation-time-adapted perturbations .

with Xin Guo, Jiequn Han and Mahan Tajrobehkar. * Journal of Computational Mathematics and Data Science (2024) vol.10, 100090. *

[29] Policy optimization for continuous reinforcement learning .

with David D. Yao and Hanyang Zhao. * Advances in Neural Information Processing Systems (Neurips 2023) vol.36, 13637-13663. *

[28] One-dependent hard-core processes and colorings of the star graph .

with Thomas Liggett. * Annals of Applied Probability (2023) vol.33, no.6A, 4341–4365. *

[27] Trading under the Proof-of-Stake protocol -- a continuous-time control approach .

with David D. Yao. * Mathematical Finance (2023) vol.33, no.4, 979-1004. *

[26] Tail probability estimates of continuous-time simulated annealing processes .

with Xun Yu Zhou. * Numerical Algebra, Control and Optimization (2023) vol.13, no.3-4, 473-485. *

[25] Fixed-domain inference for Gausian processes with Matérn covariogram on compact Riemannian manifolds .

with Didong Li and Sudipto Banerjee. * Journal of Machine Learning Research (2023) vol.24, no.101, 1-26. *

[24] Extreme order statistics of random walks
.

with Jim Pitman. * Annales de l'Institut Henri Poincaré (2023) vol.59, no.1, 97-116. *

[23] The Poisson binomial distribution -- Old & New .

with Fengmin Tang. * Statistical Science (2023) vol.38, no.1, 108-119. *

[22] Exploratory HJB equations and their convergence .

with Yuming Zhang and Xun Yu Zhou. * SIAM Journal on Control and Optimization (2022) vol.60, no.6, 3191-3216. *

[21] Ergodicity of the infinite swapping algorithm at low temperature .

with Georg Menz, André Schlichting and Tianqi Wu. * Stochastic Processes and their Applications (2022) vol 151, 519-552. *

[20] Hidden symmetries and limit laws in the extreme order statistics of the Laplace random walk .

with Jim Pitman. * Annals of Probability (2022) vol.50, no.4, 1647-1673. *

[19] Parallel search for information in continuous time -- optimal stopping and geometry of the PDE .

with T. Tony Ke, J. Miguel Villas-Boas and Yuming Zhang. * Applied Mathematics and Optimization (2022) vol.85, article 3, 1-25. *

[18] Asset selection via correlation blockmodel clustering .

with Xiao Xu and Xun Yu Zhou. * Expert Systems with Applications (2022) vol.195, 116558. *

[17] A stochastic game and stochastic free boundary problem .

with Xin Guo and Renyuan Xu. * SIAM Journal on Control and Optimization (2022) vol.60, no.2, 758-785. *

[16] On identifiability and consistency of the nugget in Gaussian spatial process models .

with Lu Zhang and Sudipto Banerjee. * Journal of the Royal Statistical Society: Series B (2021) vol.83, no.5, 1044-1070. *

[15] Arcsine laws for random walks generated from random permutations with applications to genomics .

with Xiao Fang, Han Liang Gan, Susan Holmes, Haiyan Huang, Erol Peköz and Adrian Röllin. * Journal of Applied Probability (2021) vol.58, no.4, 851-867. *

[14] The existence of maximum likelihood estimate in high-dimensional generalized linear models with binary responses .

with Yuting Ye. * Electron. J. Statist (2020) vol.14, no.2, 4028-4053. *

[13] The Buckley-Osthus model and the block preferential attachment model: statistical analysis and application .

with Xin Guo and Fengmin Tang. * Proceedings of the 37th International Conference on Machine Learning (ICML 2020) PMLR 119, 9377-9386. *

[12] Mallows ranking models: maximum likelihood estimate and regeneration .

* Proceedings of the 36th International Conference on Machine Learning (ICML 2019) PMLR 97, 6125-6134. *

[11]
Exponential ergodicity and convergence for generalized reflected Brownian motion .

* Queueing Systems: Theory and Applications (2019) vol.92, no.1, 83-101. *

[10] Renewal sequences and record chains related to multiple zeta sums .

with Jean-Jil Duchamps and Jim Pitman. * Transactions of AMS (2019) vol.371, no.8, 5731-5755. *

[9] Regenerative random permutations of integers .

with Jim Pitman. * Annals of Probability (2019) vol.47, no.3, 1378-1416. *

[8] Transporting random measures on the line and embedding excursions into Brownian motion .

with Günter Last and Hermann Thorisson. * Annales de l'Institut Henri Poincaré (2018) vol.54, no.4, 2286-2303. *

[7] The argmin process of random walks, Brownian motion and Lévy processes .

with Jim Pitman. * Electro. J. Probab (2018) vol.23, no.60, 1-35. *

[6] Optimal surviving strategy for drifted Brownian motions with absorption .

with Li-Cheng Tsai. * Annals of Probability (2018) vol.46, no.3, 1597-1650. *

[5] Tree formulas, mean first passage times and Kemeny's constant of a Markov chain .

with Jim Pitman. * Bernoulli (2018) vol.24, no.3, 1942-1972. *

[4] The spans in Brownian motion .

with Steve Evans and Jim Pitman. * Annales de l'Institut Henri Poincaré (2017) vol.53, no.3, 1108-1135. *

[3] The Slepian zero set, and Brownian bridge embedded in Brownian motion by a spacetime shift .

with Jim Pitman. * Electro. J. Probab (2015) vol.20, no.61, 1-28. *

[2] Patterns in random walks and Brownian motion .

with Jim Pitman. * Séminaire de probabilité XLVII - In Memoriam Marc Yor (2015), 49-88. *

[1] The Vervaat transform of Brownian bridges and Brownian motion .

with Titus Lupu, Jim Pitman. * Electro. J. Probab (2015) vol.20, no.51, 1-31. *

Oct, 2023: Pheonix, INFORMS .

Sept, 2023: Virtual, CityU-NUS Mean Field Game and Control Seminar .

Sept, 2023: University of Pennsylvania, Wharton Statistics seminar .

July, 2023: Lisbon, 43rd Conference on Stochastic Processes and their Applications .

May, 2023: Carnegie Mellon University, Secure Blockchain Summit .

Mar, 2023: University of Pennsylvania, Penn/Temple Probability Seminar .

Feb, 2023: Columbia University, Applied Mathematics Colloquium .

Nov, 2022: Virtual, Hong Kong-Singapore joint seminar in Financial Mathematics/Engineering .

Nov, 2022: Columbia University, Mathematical Finance seminar .

Oct, 2022: Indianapolis, INFORMS .

July, 2022: SIAM Annual Meeting, Machine Learning in Finance: Theory and Application .

May, 2022: Institute for Mathematical and Statistical Innovation, Workshop: Machine Learning and Mean Field Games .

Feb, 2022: University of Southern California, Mathematical Finance Colloquium .

Nov, 2021: Princeton University, ORFE Financial Mathematics seminar .

Oct, 2021: UCLA, Probability seminar .

July, 2021: Institute for Mathematical and Statistical Innovation, Program: Introduction to Decision Making and Uncertainty .

June, 2021: Paris, Séminaire Bachelier .

May, 2021: University of Mannheim, Probability seminar .

Dec, 2020: Virtual, Workshop on Optimization, Probability, and Simulation.

Oct, 2020: Virtual, INFORMS .

Mar, 2020: University of Michigan, Financial/Actuarial Mathematics Seminar .

Feb, 2020: Cornell University, ORIE Colloqium .

Feb, 2020: Columbia University, IEOR Department Seminar .

Jan, 2020: Baruch College, Mathematics Colloquium .

Jan, 2020: University of Utah, Mathematics Colloqium .

Jan, 2020: Northwestern University, Mathematics Colloqium .

Dec, 2019: University of Cincinnati, Probability Seminar .

Dec, 2019: University of Miami, Mathematics Colloquium .

Nov, 2019: North Carolina State University, Mathematics Colloquium .

Nov, 2019: Riverside, AMS meeting .

Nov, 2019: UCSD, Probability Seminar .

Oct, 2019: University of Washington, Probability Seminar .

Oct, 2019: Seattle, INFORMS .

Sept, 2019: UC Berkeley, Probabilty Seminar .

June, 2019: Los Angeles, ICML Oral .

Feb, 2019: UCLA, Combinatorics Seminar .

Dec, 2018: Los Angeles, Southern California Probability Symposium .

Oct, 2018: San Francisco, AMS meeting .

July, 2018: Stanford, Workshop in memory of Larry Shepp .

Feb, 2018: Stanford University, Probability Seminar .

Feb, 2018: UC Berkeley, IEOR Colloquium .

Dec, 2017: University of Chicago, Probability and Statistical physics seminar .

Nov, 2017: UCLA, Probability Seminar .

Mar, 2017: UCLA, Probability Seminar .

Mar, 2017: UC Berkeley, Probability Seminar .

July, 2016: Edmonton, IMS-FIPS Workshop .

Mar, 2016: Berkeley, Berkeley-Columbia Meeting in Engineering and Statistics .

Feb, 2015: UC Davis, Mathematical Physics and Probability Seminar .

Feb, 2015: UC Berkeley, Probability Seminar .

Oct, 2014: UC Berkeley, Student Probability/PDE Seminar .

July, 2014: Saint-Flour, 44th probability summer school.

June, 2014: San Diego, Combinatorial Stochastic Processes: A conference in celebration of Jim Pitman's 65th birthday .

July, 2013: Saint-Flour, 43rd probability summer school.

Sept, 2013: UC Berkeley, SGSA Student Seminar .

In Fall 2021, I will teach IEOR E4706: Foundations of Financial Engineering.