Luh, Kyle

Publications

selected publications

conference proceeding
- Robustness Implies Generalization via Data-Dependent Generalization Bounds. 10866-10894. 2022
- A Fast Spectral Algorithm for Mean Estimation with Sub-Gaussian Rates 2020
- An Improved Lower Bound for Sparse Reconstruction from Subsampled Hadamard Matrices. Annual Symposium on Foundations of Computer Science. 1564-1567. 2019
- Random matrices: l(1) concentration and dictionary learning with few samples. Annual Symposium on Foundations of Computer Science. 1409-1425. 2015
journal article
- Rate of convergence in multiple SLE using random matrix theory. Random Matrices: Theory and Applications. 2025
- Eigenvalue gaps of the Laplacian of random graphs 2024
- An Improved Lower Bound for Sparse Reconstruction from Subsampled Walsh Matrices. Discrete Analysis. 1-9. 2023
- Circular law for random block band matrices with genuinely sublinear bandwidth. Journal of Mathematical Physics. 2021
- On the counting problem in inverse Littlewood-Offord theory. Journal of London Mathematical Society. 1333-1362. 2021

Teaching

courses taught

MATH 2001 - Introduction to Discrete Mathematics
Primary Instructor - Fall 2023
Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Credit not granted for this course and MATH 2002.
MATH 3170 - Combinatorics 1
Primary Instructor - Fall 2022
Covers basic methods and results in combinatorial theory. Includes enumeration methods, elementary properties of functions and relations, and graph theory. Emphasizes applications.
MATH 4510 - Introduction to Probability Theory
Primary Instructor - Fall 2020 / Spring 2024
Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains if time permits. Degree credit not granted for this course and APPM 3570 or ECEN 3810 or MATH 3510. Same as MATH 5510.
MATH 4520 - Introduction to Mathematical Statistics
Primary Instructor - Spring 2021
Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distribution-free methods. Same as MATH 5520 and STAT 4520 and STAT 5520.
MATH 4530 - Theoretical Foundations of Data Science
Primary Instructor - Spring 2023
Introduces theoretical concepts from mathematics, statistics, and computer science required to understand and analyze data. Topics include randomized algorithms, machine learning, streaming, sketching, clustering, random matrices and graphs, graphical models and compressed sensing.

MATH 5510 - Introduction to Probability Theory
Primary Instructor - Fall 2020 / Spring 2024
Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains if time permits. Same as MATH 4510.

MATH 5520 - Introduction to Mathematical Statistics
Primary Instructor - Spring 2021
Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distribution-free methods. Department enforced prerequisite: one semester calculus-based probability course, such as MATH 4510 or APPM 3570. Recommended prerequisite: previous coursework equivalent to APPM 3570 or STAT 3100 or MATH 4510; minimum grade of C- for all. Same as STAT 4520 and MATH 4520 and STAT 5520.

MATH 6310 - Introduction to Real Analysis 1
Primary Instructor - Fall 2023
Develops the theory of Lebesgue measure and the Lebesgue integral on the line, emphasizing the various notions of convergence and the standard convergence theorems. Applications are made to the classical L^p spaces. Department enforced prerequisite: MATH 4001. Instructor consent required for undergraduates.

MATH 6350 - Functions of a Complex Variable 1
Primary Instructor - Fall 2022
Focuses on complex numbers and the complex plane. Includes Cauchy-Riemann equations, complex integration, Cauchy integral theory, infinite series and products, and residue theory. Department enforced prerequisite: MATH 4001. Instructor consent required for undergraduates.

MATH 6550 - Introduction to Stochastic Processes
Primary Instructor - Spring 2022
Systematic study of Markov chains and some of the simpler Markov processes, including renewal theory, limit theorems for Markov chains, branching processes, queuing theory, birth and death processes, and Brownian motion. Applications to physical and biological sciences. Department enforced prerequisite: MATH 4001 or MATH 4510 or APPM 3570 or APPM 4560. Instructor consent required for undergraduates. Same as APPM 6550.

STAT 4520 - Introduction to Mathematical Statistics
Primary Instructor - Spring 2021
Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distribution-free methods. Same as STAT 5520 and MATH 4520 and MATH 5520.

STAT 5520 - Introduction to Mathematical Statistics
Primary Instructor - Spring 2021
Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distribution-free methods. Department enforced prerequisite: one semester calculus-based probability course, such as MATH 4510 or APPM 3570. Recommended prerequisite: previous coursework equivalent to APPM 3570 or STAT 3100 or MATH 4510; minimum grade of C- for all. Same as STAT 4520 and MATH 4520 and MATH 5520.

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Background

education and training

Ph.D., Yale University 2017
M.S., Yale University 2015
M.S., Yale University 2012
B.A., Harvey Mudd College 2011

awards and honors

Ralph E. Powe Junior Faculty Enhancement Award, conferred by Oak Ridge Associated Universities, 2021

VIVO

Positions

Research Areas

Publications

selected publications

conference proceeding

journal article

Teaching

courses taught

Background

education and training

awards and honors

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