I am an assistant professor in the Department of Mathematics at Duke University. I study problems in probability theory, partial differential equations, and applied math. I am particularly interested in the asymptotic behavior of stochastic partial differential equations.

Before coming to Duke, from 2020 to 2023 I was an NSF postdoc at NYU Courant, sponsored by Jean-Christophe Mourrat and Yuri Bakhtin. I completed my Ph.D. at Stanford in 2020, advised by Lenya Ryzhik.

Along with the other probabilists in the department, I help organize the Duke Probability Seminar. Everyone is welcome to attend.

- Additive-multiplicative stochastic heat equations, stationary solutions, and Cauchy statistics (with Chiranjib Mukherjee). Submitted, 2024. [arXiv]
- Branching Brownian motion with generation-dependent diffusivity and nonlocal partial differential equations (with Lenya Ryzhik). Submitted, 2023. [arXiv]
- Jointly stationary solutions of periodic Burgers flow (with Yu Gu). Submitted, 2023. [arXiv]
- The 2D nonlinear stochastic heat equation: pointwise statistics and the decoupling function (with Cole Graham). Submitted, 2023. [arXiv]
- Uniqueness and root-Lipschitz regularity for a degenerate heat equation (with Cole Graham). Submitted, 2023. [arXiv]
- Localization length of the \(1+1\) continuum directed polymer (with Yu Gu and Liying Li). Annales Henri Poincaré
**24**(2023), pp. 2537–2555. [arXiv, doi] - Invariant measures for stochastic conservation laws on the line (with Theodore D. Drivas, Cole Graham, Joonhyun La, and Lenya Ryzhik). Nonlinearity
**36**(2023), no. 9, pp. 4553–4584. [arXiv, doi] - Fluctuation exponents of the KPZ equation on a large torus (with Yu Gu and Tomasz Komorowski). Communications on Pure and Applied Mathematics
**76**(2023), no. 11, pp. 3104–3149. [arXiv, doi] - Local versions of sum-of-norms clustering (with Jean-Christophe Mourrat). SIAM Journal on Mathematics of Data Science (SIMODS)
**4**(2022), no. 4, pp. 1250–1271. [arXiv, doi] - A quenched local limit theorem for stochastic flows (with Yu Gu). Journal of Functional Analysis
**282**(2022), no. 6, 109372. [arXiv, doi] - Sum-of-norms clustering does not separate nearby balls (with Jean-Christophe Mourrat). Accepted at Journal of Machine Learning Research, 2024. [arXiv]
- A forward-backward SDE from the 2D nonlinear stochastic heat equation
(with Yu Gu). Annals of Probability
**50**(2022), no. 3, pp. 1204–1253. [arXiv, doi] - Viscous shock solutions to the stochastic Burgers equation (with Lenya Ryzhik). Archive for Rational Mechanics and Analysis
**242**(2021), no. 2, pp. 937–971. [arXiv, doi] - The continuum parabolic Anderson model with a half-Laplacian and periodic noise. Electronic Communications in Probability
**25**(2020), paper no. 64. [arXiv, doi] - Existence of stationary stochastic Burgers evolutions on \(\mathbf{R}^2\) and \(\mathbf{R}^3\). Nonlinearity
**33**(2020), no. 12, pp. 6480–6501. [arXiv, doi] - Stationary solutions to the stochastic Burgers equation on the line (with Cole Graham and Lenya Ryzhik). Communications in Mathematical Physics
**382**(2021), no. 2, pp. 875–949. [arXiv, doi] - Tightness of Liouville first passage percolation for \(\gamma\in (0,2)\)
(with Jian Ding, Julien Dubédat, and Hugo Falconet). Publications Mathématiques de l'IHÉS
**132**(2020), pp. 353–403. [arXiv, doi] - Subsequential scaling limits for Liouville graph distance
(with Jian Ding). Communications in Mathematical Physics
**376**(2020), pp. 1499–1572. [arXiv, doi] - Fluctuations of the solutions to the KPZ equation in dimensions three and higher
(with Yu Gu, Lenya Ryzhik, and Ofer Zeitouni). Probability Theory and Related Fields
**176**(2020), no. 3–4, pp. 1217–1258. [arXiv, doi] - Constructing a solution of the \((2+1)\)-dimensional KPZ equation
(with Sourav Chatterjee). Annals of Probability
**48**(2020), no. 2, pp. 1014–1055. [arXiv, doi] - The random heat equation in dimensions three and higher: the homogenization viewpoint
(with Yu Gu, Lenya Ryzhik, and Ofer Zeitouni). Archive for Rational Mechanics and Analysis
**242**(2021), no. 2, pp. 827–873. [arXiv, doi] - Liouville first-passage percolation: subsequential scaling limit at high temperature
(with Jian Ding). Annals of Probability
**47**(2019), no. 2, pp. 690–742. [arXiv, doi] - Expected regularized total variation of Brownian motion. Unpublished. [arXiv]

- Curiosity-Based Biophysics Projects in a High School Setting with Graduate Student Mentorship (Cooper J Galvin,
Katherine N. Liu,
Andrew S. Kennard,
Sahil K. Tembulkar,
Alexander Dunlap,
Tao A. G. Large,
Thao Pham,
Derek Le,
Aurora Alvarez-Buylla,
Helen Nguyen,
Ezequiel Ponce,
Sophia Tran,
Nikki Nguyen,
Christina Ngo,
Christina Tran,
Gabriela Huynh,
Patrick Allamandola,
Zev Bryant). The Biophysicist
**2**(2021), no. 1. [doi]

- Nonlinear weak-noise stochastic heat equations in two dimensions at the Probability and the City Seminar, April 2022
- A forward-backward SDE from the 2D nonlinear stochastic heat equation at the Junior Integrable Probability Seminar, December 2020
- Stationary and shock solutions for the stochastic Burgers equation at the Stanford Probability Seminar, June 2020
- Constructing (2+1)-dimensional KPZ evolutions at the BIRS workshop Interacting Particle Systems and Parabolic PDEs, August 2018

Some mathematical visualizations (require a reasonably modern [in 2016] browser, e.g. Firefox or Chrome).

- Spring 2024 (March 20–April 17): Minicourse on Stochastic PDE
- Fall 2023: Math 541 Applied Stochastic Processes
- Spring 2023: MATH-GA 2500 Partial Differential Equations
- Fall 2022: MATH-UA 262 Ordinary Differential Equations
- Spring 2022: MATH-UA 233 Theory of Probability
- Fall 2021: MATH-UA 120 Discrete Mathematics

- Email: dunlap at math decimal duke decimal edu
- Office: Physics 297
- ORCID
- Pronouns: he/him