Alex Dunlap's home page
I am an NSF postdoc at NYU Courant, sponsored by JeanChristophe Mourrat and Yuri Bakhtin. I study problems in probability theory, partial differential equations, and applied math. I got my Ph.D. from Stanford in 2020, advised by Lenya Ryzhik.
Math papers and preprints
 A quenched local limit theorem for stochastic flows (with Yu Gu). Submitted, 2021. [arXiv]
 Sumofnorms clustering does not separate nearby balls (with JeanChristophe Mourrat). Submitted, 2021. [arXiv]
 A forwardbackward SDE from the 2D nonlinear stochastic heat equation
(with Yu Gu). Submitted, 2020. [arXiv]
 Viscous shock solutions to the stochastic Burgers equation (with Lenya Ryzhik). Archive for Rational Mechanics and Analysis (2021). [arXiv, doi]
 The continuum parabolic Anderson model with a halfLaplacian 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 (2021). [arXiv, doi]
 Liouville firstpassage 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 Unpublished.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]
Published report

CuriosityBased 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 AlvarezBuylla,
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]
Recorded talks
Expository
Some mathematical visualizations (require a reasonably modern [in 2016] browser, e.g. Firefox or Chrome).
Teaching
Fall 2021: MATHUA 0120 Discrete Mathematics
Contact
 Email: alexander DOT dunlap AT cims DOT nyu DOT edu.
 Office: WWH 1005B.
 ORCID
 Pronouns: he/him
Links