## About

I am a final-year PhD candidate at Stanford University in the Operations Research group within Department of Management Science and Engineering, where I am fortunate to be advised by Peter Glynn and Jose Blanchet. Previously, I received my bachelor degree in Mathematics from University of Science and Technology of China (USTC). My email is quyanlin at stanford dot edu.

## Research

Broadly speaking, I am interested in analyzing modern complex systems where uncertainty plays an essential role in performance analysis and decision making.
These systems include not only stochastic models utilized in operations research (OR) and management science (MS) but also stochastic algorithms utilized in optimization and simulation.
To fundamentality facilitate this analysis, I develop novel theories and algorithms in the realm of general state-space **Markov chains**.

*MC Convergence Trilogy*

#### Deep Learning for Computing Convergence Rates of Markov Chains

with Jose Blanchet and Peter Glynn, *submitted*, [arXiv]

- The first general-purpose algorithm to bound the convergence

#### Computable Bounds on Convergence of Markov Chains in Wasserstein Distance

with Jose Blanchet and Peter Glynn, *submitted*, [arXiv]

- The theoretical foundation of the above algorithm
- Applied Probability Society Best Student Paper Prize, 2023
- Applied Probability Society Conference Best Poster Award, 2023

#### Estimating the Convergence Rate to Equilibrium of a Markov Chain via Simulation

with Jose Blanchet and Peter Glynn, *preprint*

- Another sample-based algorithm to bound the convergence

#### Strong Limit Interchange Property of a Sequence of Markov Processes

with Jose Blanchet and Peter Glynn, *work in progress*

- General framework to verify \(X_n(t)\Rightarrow X_\infty(\infty)\) as \(n,t\rightarrow\infty\)

#### On a New Characterization of Harris Recurrence for Markov Chains and Processes

with Peter Glynn, *Mathematics*, 2023

#### Bias of Markov Chain Sample Quantile

with Peter Glynn, *preprint*

#### Uniform Edgeworth Expansion for Markov Chains

with Peter Glynn, *preprint*

#### Double Distributionally Robust Bid Shading for First Price Auctions

with Ravi Kant, Yan Chen, Brendan Kitts, San Gultekin, Aaron Flores, Jose Blanchet, *submitted*, manuscript available upon request

- How should we bid if we are uncertain about multiple factors?

## Teaching

Winner of the 2024 Centennial Teaching Assistant Award

Teaching assistant for the following MS&E courses at Stanford

*Ragnarök*

This is a fun project related to Markov chain, stochastic simulation, and cube. Perfect order can be reached in twenty moves (God's number). What about complete chaos? How hard is it to scramble Rubik’s Cube? Currently, we have \(t_{\text{mix}}\geq26\). A better bound is coming soon.