The research of the faculty covers a broad area of probability theory, mathematical statistics, and their applications.
- Alexander, Kenneth: Probability models in statistical mechanics: lattice models (Ising model, Potts model, percolation, etc.), phase transitions, disordered models.
- Arratia, Richard: Probability, especially as related to combinatorics and number theory, coupling, and approximation.
- Chen, Xiaohui: High-dimensional statistics, machine learning, and optimal transport.
- Dimitrov, Evgeni: Integrable probability.
- Fulman, Jason: Markov chains, probability on algebraic structures, random matrix theory, Stein’s method.
- Goldstein, Larry: Distributional approximation and Stein’s method, high dimensional statistics, concentration inequalities, sampling schemes in epidemiology, statistical efficiency, optimal stopping.
- Lototsky, Sergey: Stochastic partial differential equations, optimal nonlinear filtering of diffusion processes, statistical inference for continuous-time processes.
- Lv, Jinchi (Marshall School of Business): statistics, machine learning, data science, business applications, and artificial intelligence and blockchain.
- Ma, Jin: Stochastic analysis, stochastic differential equations, stochastic control theory, mathematical finance and insurance.
- Minsker, Stanislav (Stas): Statistical learning theory, non-parametric statistics, concentration inequalities, mathematical finance.
- Sun, Fengzhu (Department of Quantitative and Computational Biology): Quantitative and computational biology, probability, statistics.
- Zhang, Jianfeng: Stochastic analysis, backward stochastic differential equations, stochastic numerics, and mathematical finance.
- Baxendale, Peter: Stochastic dynamical systems; equilibrium, stability, and bifurcation for solutions of stochastic differential equations; applications to stochastic neuronal models.
- Mikulevicius, Remigijus (Remi): Stochastic differential equations, stochastic analysis.
- Waterman, Michael (Department of Quantitative and Computational Biology): Molecular and computational biology, probability, statistics.
- Gao, Lan: High-Dimensional Statistics, High-Dimensional Inference, and Causal Inference.
- Heilman, Steven: High-Dimensional Probability, Concentration Inequalities, Theoretical Computer Science, Random Graphs.
- Rychnovsky, Mark: Random Matrix Theory, Statistical Mechanics, and Kardar Parisi Zhang Universality, as well as combinatorics and epidemiology.
- Xia, Weixuan: investment decisions under incomplete preferences, exotic derivatives, cryptocurrency markets, optimal control of set-valued stochastic processes, Lévy functionals and illiquidity measures, and neural network architectures applicable in these areas.
- Valentin Tissot-Daguette, visiting Ph.D. student from Princeton University (Host: J. Zhang).
CURRENT Ph.D. STUDENTS
- Atiqah Almuzaini (Ma)
- Xinze Du (Lv)
- Thejani Gamage (Ma)
- Cora Liang (Goldstein/Sun)
- Oleksandra Lymar (Goldstein/Minsker)
- Bixing Qiao (Zhang)
- Gaozhan Wang (Ma/Zhang)
- Bo Wu (Alexander)
CURRENT MASTERS STUDENTS:
CURRENT UNDERGRADUATE STUDENTS:
- Sam Zhang (Heilman)
- Math Finance Colloquium
- Probability and Statistics Seminar. Some of the recent lectures are available here.
- Math 705 (Graduate Student Probability Seminar)
RECENT Ph.D. GRADUATES, THEIR ADVISORS, AND DISSERTATIONS
- Arslan, Aykut (Lv/Yingying Fan), High-Dimensional Rescaled Square-Root Lasso under Distributional Shift and its Robustness
- Iseri, Melih (Zhang), Set Values for Mean Field Games and Set Valued PDEs
- Karakus, Abdullah (Alexander), First Passage Percolation in a Correlated Environment
- Paguyo, J. E. (Fulman), Limit Theorems for Three Random Discrete Structures via Stein’s Method
- Tan, Ying (Ma), Stochastic Two-point Boundary Value Problem and Application in Kyle-Back Equilibrium Model
- Wang, Lijia (Goldstein), Statistical Citation Network Analysis and Asymmetric Error Controls
- Yao, Shunan (Minsker), New Methods For Asymmetric Classification and Robust Bayesian Inference
- Liu, Jinting (Goldstein/Sun), Selective Inference With Confident Directions
- Pollok, Austin (Zhang), High-Frequency Kelly Criterion and Fat-Tails: Gambling with an Edge
- Shah, Apoorva (Lototsky), Gaussian Free Fields and Stochastic Parabolic Equations
- Tarter, Alex (Goldstein/Heilman), Dimension Reduction Techniques for Noise Stability Theorems
- Vossler, Patrick (Yingying Fan/Lv), Nonparametric Ensemble Learning and Inference
- Wu, Yusheng (Lototsky/Tong), Asymptotic Properties of Two Network Problems with Large Random Graphs
- Feng, Pengbin (Ma/Zhang), Dynamic Network Model for Systemic Risk
- Gangopadhyay, Ujan (Alexander), Fluctuations of the Transverse Increments in the Two-dimensional First-passage Percolation Model
- Luo, Man (Ma), Topics on Dynamic Limit Order Book and its Related Computation
- Rahmani, John (Fulman), Mixing Times for the Commuting Chain
- Wang, Lang (Minsker), Robust Estimation of High Dimensional Parameters
- Wu, Wenqian (Ma), Topics on Set-Valued Backward Stochastic Differential Equations
- Zhu, Zimu (Zhang), Some Topics on Continuous Time Principal-Agent Problem
Aronowitz, Julian (Bartroff), Finite Sample Bounds in Group Sequential Analysis via Stein’s Method
Phonsom, Chukiat (Mikulevicius), On Stochastic Integro-Differential Equations
- Ruan, Jie (Zhang), Numerical Methods for High-Dimensional Path-Dependent PDEs Driven by Stochastic Volterra Equations
- Wei, Xiaohan (Minsker/Neely), Part I: Asynchronous optimization over weakly coupled renewal systems. Part II: High dimensional estimation under weak moment assumptions
- Wu, Hao (Zhang/Lv), Statistical Insights into Deep Learning and Flexible Causal Inference
- Demirkaya, Emre (Yingying Fan/Goldstein/Lv), Reproducible Large-Scale Inference in High-Dimensional Nonlinear Models
- He, Xinrui (Bartroff), Asymptotically optimal sequential multiple testing with (or without) prior information on the number of signals
- Ozdemir, Alperen (Fulman), On Limiting Distribution and Convergence Rates of Random Processes Defined Over Discrete Structures
- Wiroonsri, Nathakhun (Goldstein), Steins’ Method via Approximate Zero Biasing and Positive Association with Applications to the Combinatorial Central Limit Theorem and Statistical Physics
- Xu, Fanhui (Mikulevicius), On the parabolic Kolmogorov integro-differential equation and its applications
- Bhattacharjee, Chinmoy (Goldstein), Stein’s Method and its Applications in Strong Embeddings and Dickman Approximations
- Kim, Gene B (Fulman), Distribution of Descents in Matchings
- Kim, Hyun-Jung (Lototsky), Time-Homogeneous Parabolic Anderson Model
- Noh, Eunjung (Ma), Equilibrium Model of Limit Order Book and Optimal Execution Problem
- Ozel, Enes (Fulman), Cycle Structures of Permutations with Restricted Positions
- Sun, Rentao (Ma), Conditional Mean-Field Stochastic Differential Equations and Their Applications
- Wang, Jian (Lototsky), Statistical Inference For Second-Order Ordinary Differential Equation Driven by Additive Gaussian White Noise
- Hankin, Michael (Bartroff), Sequential Testing of Multiple Hypotheses With FDR Control Under Dependence
- Nguyen, Dinh (Fulman), Random Walks on Finite Groups and Their Irreducible Representations
- Wu, Cong (Zhang), Controlled McKean-Vlasov Equations and Related Topics
- Xing, Xiaojing (Ma), Optimal Investment and Dividend under Sparre Andersen Model
- Kang, Yongjian (Lv/Zhang), Large-Scale Inference in Multiple Gaussian Graphical Models
- Karnam, Chandrasekhar (Ma/Zhang), Dynamic Approaches for some Time Inconsistent Problems
- Tsilifis, Panagiotis (Ghanem/Mikulevicius), Design, Adaptation and Variational Methods in Uncertainty Quantification
- Xie, Weisheng (Ma), Stochastic Differential Equations Driven by Fractional Brownian Motion and Poisson Point Processes
- Keller, Christian (Zhang), Pathwise Stochastic Analysis and Related Topics
- Ren, Haining (Fulman), Convergence Rates of i-Cycles After an m-Shelf Shuffle
- Zhang, Tian (Ma), Optimal Investment and Reinsurance Problems and Related Non-Markovian FBSDEs With Constraints
- Zheng, Zemin (Goldstein/Lv), High-Dimensional Latent Variable Thresholded Regression
- Daley, Timothy (Smith/Waterman), Non-Parametric Models For Large Capture-Recapture Experiments With Applications to DNA Sequencing
- Bessam, Diogo (Lototsky), Large Deviations Rates in a Gaussian Setting and Related Topics
- Ekren, Ibrahim (Zhang), Path-Dependent Partial Differential Equations and Related Topics
- Islak, Umit (Fulman), Concentration Inequalities with Couplings from Stein’s Method
- Sokolov, Grigory (Tartakovsky/Lototsky), Multi-Population Optimal Change-Point Detection
- Zhuo, Jia (Zhang), Probabilistic Numerical Methods for Fully Nonlinear PDEs and Related Topics
- Chubatiuk, Alona (Schumitzky), Nonparametric Estimation of an Unknown Probability Distribution Using Maximum Likelihood and Bayesian Approaches
- Marinov, Radoslav (Fulman), Applications of Stein’s Method on Statistics of Random Graphs
- Pham, Triet (Zhang), Zero-Sum Stochastic Differential Games in Weak Formulation and Related Norms for Semi-Martingales
- Pike, John (Fulman), Eigenfunctions for Random Walks on Hyperplane Arrangements
- Song, Jinlin (Bartroff), Time-Sequential Testing for Multiple Hypotheses
- Wang, Huanhuan (Ma), Asset Management with Incomplete Information
- Wang, Xin (Ma), Nonlinear Expectations for Continuous Time Model with Jumps and Applications
- Xu, Li (Lototsky), Parameter Estimate for Hyperbolic SPDE’s with Stochastic Coefficients
- Yildirim, Gokhan (Alexander), On the Depinning Transition of the Directed Polymer in a Random Environment With a Defect Line
- Zhong, Jie (Lototsky), Second Order in Time Stochastic Evolution Equation and Wiener Chaos Approach
- DeSalvo, Stephen (Arratia), Probabilistic Divide-and-Conquer: A New Method for Exact Simulation and Lower Bound Expansions for Random Bernoulli Matrices via Novel Integer Partitions
- Du, Jie (Zhang), Stochastic Games on Stopping Times
- Ghosh, Subhankar (Goldstein), Couplings for Berry-Esseen Bounds and Concentration Inequalities
- Kaligotla, Sivaditya (Lototsky), Asymptotic Problems in Stochastic Partial Differential Equations: A Wiener Chaos Approach
- Lin, Ning (Lototsky), Estimation of Coefficients in Stochastic Differential Equations
- Moers, Michael (Lototsky), Statistical Inference of Stochastic Differential Equations Driven by Gaussian Noise
- Nibert, Joel (Baxendale), Invariant Measures of a Stochastic Predator-Prey Model
- Xu, Shanshan (Lototsky/Wilcox), Initiative Non-Parametric Multivariate Regression Hypothesis Testing
- Chen, Jianfu (Ma), Regime Switch Term Structure Model With Forward-Backward Stochastic Differential Equations
- Lin, Wei (Goldstein), Survival Analysis With Missing Data and High Dimensionality
- Wang, Xinyang (Ma/Zhang), Dynamic Model for Limit Order Books and Optimal Liquidation Problems
- Yun, Youngyun (Ma), Analysis of Correlated Defaults and Joint Default Probability in a Contagion Model
- Liu, Wei (Lototsky), Statistical Inference for Stochastic Hyperbolic Equations
- Zhang, Changyong (Mikulevicius), Numerical Weak Approximation of Stochastic Differential Equations Driven by Levy Processes
- Knape, Mathias (Mikulevicius/Zapatero), A General Equilibrium Model for Exchange Rates and Asset Prices in an Economy Subject to Jump-Diffusion Uncertainty
- Pehlivan, Lerna (Fulman), On Top to Random Shuffles, no Feedback Card Guessing and Fixed Points of Permutations
- Polunchenko, Aleksey (Mikulevicius/Tartakovsky), Quickest Change Detection with Applications to Distributed Multi-Sensor Systems
- Ross, Nathan (Fulman), Exchangeable Pairs in Stein’s Method of Distributional Approximation
THE (FIRST) JOBS OF SOME OF OUR RECENT Ph.D. GRADUATES
- Aykut Arslan: Lecturer, USC
- Melih Iseri: Postdoc at the University of Michigan
- J.E. Paguyo: Postdoc at McMaster University (Hamilton, Ontario, Canada)
- Ying Tan: Postdoc at UCSB
- Austin Pollok: Assistant Professor of Clinical Data Science and Operations, USC
- Apoorva Shah: Data Scientist at Neal Analytics
- Alex Tarter: Statistician at the NASS (USDA)
- Patrick Vossler: Postdoctoral Scholar, Stanford University
- Pengbin Feng: Research Scientist at Amazon.
- Ujan Gangopadhyay: Postdoc at Natl. Univ. of Singapore.
- Man Luo: Quant Researcher at Guotai Junan Securities Asset Management (Shanghai, China).
- John Rahmani: Data Scientist at Accenture (San Diego, CA).
- Wenqian Wu: Quant Trader at Guotai Junan Securities (Shanghai, China).
- Zimu Zhu: Postdoc at UCSB.
- Julian Aronowitz: Data Scientist at Palo Alto Networks
- Chukiat Phonsom: Alexandria Technology, Research and Investment
- Jie Ruan: Facebook
- Xiaohan Wei: Facebook
- Emre Demirkaya: Assistant Professor at the Haslam College of Business, University of Tennessee
- Xinrui He: Statistician at Acumen/The SPHERE Institute
- Alperen Ozdemir: Postdoc, Department of Mathematics, Georgia Tech
- Fanhui Xu: Postdoctoral Associate, Carnegie Mellon University
- Nathakhun Wiroonsri: Instructor, King Mongkut University of Technology Thonburi (Bangkok, Thailand)
- Chinmoy Bhattacharjee: Postdoc, IMSV, University of Bern
- Gene Kim: Lecturer, USC; currently Lecturer at Stanford
- Hyun-Jung Kim: Postdoc, Illinois Institute of Technology
- Eunjung Noh: Hills Assistant Professor, Rutgers Univ
- Enes Ozel: Adjunct Assistant Professor, UCLA
- Rentao Sun: Data scientist, The Data Incubator
- Michael Hankin: Google
- Dinh Nguyen: Polytechnic School (Pasadena)
- Cong Wu: Quantitative Associate at Wells Fargo
- Xiaojing Xing: Wells Fargo (Charlotte, NC)
- Yongjian Kang: Google
- Chandrasekhar Karnam: Morgan Stanley
- Panagiotis Tsilifis: Postdoc in the Viterbi School of Engineering at USC
- Weisheng Xie: Wells Fargo (Charlotte, NC)
- Christian Keller: Postdoc at the University of Michigan
- Haining Ren: Pixalate (Santa Monica, CA)
- Tian Zhang: Education Management Systems
- Zemin Zheng: Assistant Professor at the Chinese University of Science and Technology
- Diogo Bessam: Postdoc at PUC-RJ/IMPA (Brasil)
- Ibrahim Ekren: Postdoc at ETH Zurich
- Umit Islak: Postdoc at the University of Minnesota – Twin Cities
- Grigory Sokolov: Postdoc at SUNY Binghamton
- Jia Zhuo: Morgan Stanley
- Alona Chubatiuk: Postdoc at Children’s Hospital LA
- Triet Pham: Postdoc at Rutgers
- John Pike: Postdoc at Cornell
- Jinlin Song: Researcher at the Analysis Group
- Huanhuan Wang: Capital One
- Xin Wang: Morgan Stanley
- Li Xu: Google
- Gokhan Yildirim: Lecturer at USC
- Jie Zhong: Postdoc at Ritsumeikan University (Japan); currently Assistant Professor at Cal State LA
- Stephen DeSalvo: Postdoc at UCLA; currently at Google
- Jie Du: Guggenheim Partners
- Subhankar Ghosh: SAS Statistical Software
- Sivaditya Kaligotla: Bloomberg LP
- Ning Lin: Citigroup
- Michael Moers: Deutsche Bank
- Joel Nibert: Lecturer at USC
- Jianfu Chen: Union Bank of California
- Wei Lin: Postdoc at UPenn
- Xinyang Wang: Morgan Stanley
- Youngyun Yun: Union Bank of California
- Wei Liu: American Express
- Changyong Zhang: Postdoc at Salzburg University
- Mathias Knape: Goldman Sachs
- Lerna Pehlivan: Lecturer at York University
- Aleksey Polunchenko: Postdoc at USC
- Nathan Ross: Postdoc at UC Berkeley
The next step for some of our undergraduate and masters students:
- Chuhuan Huang: Masters student, worked with Steven Heilman; in Fall 2023
started Ph.D. program in math at Johns Hopkins University,
- Benny Cohen: Undergraduate student, worked with Steven Heilman; in Fall 2023 started Ph.D. program in Mechanical Engineering at USC.
- Jake Freeman: Undergraduate student, worked with Steven Heilman; in Fall 2023 started Ph.D. program in ORFE at Princeton. See here for even more.