- Email: ygu7@umd.edu

- Office Address:
2313 Kirwan Hall

- I am an associate professor at University of Maryland, College Park. I obtained my PhD from Columbia in 2014 and did a postdoc at Stanford in 2014-2017. I was a research member of MSRI in fall 2015. I was an assistant professor at CMU in 2017-2021.
- My general interest is in the study of random dynamics and nonequilibrium statistical mechanics. I have worked on stochastic homogenization, wave propagation in random media, and more recently on stochastic PDE.
- My research has been supported by NSF grant DMS-1613301/1807748/1907928/CAREER-2042384.

- STAT 600 Probability Theory I, UMD fall 2024.
- STAT 410 Introduction to Probability Theory, spring 2024.
- MATH 858T Stochastic Methods with Applications, UMD spring 2023.
- STAT 600 Probability Theory I, UMD fall 2022.
- A course on the analysis on Gaussian space taught at UMD in spring 2022. Lecture note can be found here.
- A note on stochastic heat equation and KPZ equation, which can be found here.

- Fluctuation exponents of the half-space KPZ at stationarity. (with R. Tao), submitted, 2024.
- Integration by parts and invariant measure for KPZ. (with J. Quastel), submitted, 2024.
- Periodic Pitman transforms and jointly invariant measures. (with I. Corwin, E. Sorensen), submitted, 2024.
- Some recent progress on the periodic KPZ equation. (with T. Komorowski), submitted, 2024.
- Jointly stationary solutions of periodic Burgers flow. (with A. Dunlap),
*Journal of Functional Analysis*,**287**(2024), no. 12, 110656. - Effective diffusivities in periodic KPZ. (with T. Komorowski), to appear in
*Probability Theory and Related Fields*, 2024. - Localization length of the 1+1 continuum directed random polymer. (with A. Dunlap, L. Li),
*Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics*,**24**, 2537–2555 (2023). - Fluctuations of the winding number of a directed polymer on a cylinder. (with T. Komorowski),
*SIAM Journal on Mathematical Analysis*,**55**(2023), No. 4, pp. 3262-3286. - Another look at the Balázs-Quastel-Seppäläinen theorem. (with T. Komorowski),
*Transactions of the American Mathematical Society*,**376**(2023), 2947-2962. - Gaussian fluctuations of replica overlap in directed polymers. (with T. Komorowski),
*Electronic Communications in Probability*, 27: 1--12 (2022). - Fluctuation exponents of the KPZ equation on a large torus. (with A. Dunlap, T. Komorowski),
*Communications on Pure and Applied Mathematics*,**76**, 11 (2023), pp. 3104-3149. - High temperature behaviors of the directed polymer on a cylinder. (with É. Brunet, T. Komorowski),
*Journal of Statistical Physics*,**186**, 48 (2022). - A quenched local limit theorem for stochastic flows. (with A. Dunlap),
*Journal of Functional Analysis*,**282**(2022), no. 6, 109372. - KPZ on torus: Gaussian fluctuations. (with T. Komorowski),
*Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques*, 2024, Vol. 60, No. 3, 1570–1618. - Long-time behavior for a nonlocal model from directed polymers. (with C. Henderson),
*Nonlinearity*, 2022**36**(2), 902. - A forward-backward SDE from the 2D nonlinear stochastic heat equation. (with A. Dunlap),
*Annals of Probability*,**50**(2022), No. 3, pp. 1204-1253. - Gaussian fluctuations from random Schrödinger equation. (with T. Komorowski),
*Communications in Partial Differential Equations*,**46**(2021), No. 2, pp. 201-232. - A PDE hierarchy for directed polymers in random environments. (with C. Henderson),
*Nonlinearity*,**34**(2021), pp. 7335–7370. - Fluctuations of a nonlinear SHE in dimensions three and higher. (with J. Li),
*SIAM Journal on Mathematical Analysis*,**52**(2020), No. 6, pp. 5422-5440. - Moments of the 2D SHE at criticality. (with J. Quastel, L.-C. Tsai),
*Probability and Mathematical Physics*,**2**(2021), No. 1, pp. 179-219. - Gaussian fluctuations from the 2D KPZ equation.
*Stochastics and Partial Differential Equations: Analysis and Computations*,**8**(2020), pp. 150-185. - Fluctuations of the solutions to the KPZ equation in dimensions three and higher. (with A. Dunlap, L. Ryzhik, O. Zeitouni),
*Probability Theory and Related Fields*,**176**(2020), pp. 1217-1258. - The random heat equation in dimensions three and higher: the homogenization viewpoint. (with A. Dunlap, L. Ryzhik, O. Zeitouni),
*Archive for Rational Mechanics and Analysis*,**242**(2021), pp. 827–873. - The 1D Schrödinger equation with a spacetime white noise: the average wave function.
*ESAIM: Probability and Statistics*,**23**(2019), pp. 338-349. - Fluctuations of random semi-linear advection equations. (with T. Komorowski, L. Ryzhik),
*SIAM Journal on Mathematical Analysis*,**50**(2018), No. 5, pp. 5293-5336. - Another look into the Wong-Zakai theorem for stochastic heat equation. (with L.-C. Tsai),
*Annals of Applied Probability*,**29**(2019), No. 5, pp. 3037-3061. - Chaos expansion of 2D parabolic Anderson model. (with J. Huang),
*Electronic Communications in Probability*,**23**(2018), No. 26, pp. 1-10. - The Edwards-Wilkinson limit of the random heat equation in dimensions three and higher. (with L. Ryzhik, O. Zeitouni),
*Communications in Mathematical Physics*,**363**(2018), No. 2, pp. 351-388. - The Schrödinger equation with spatial white noise: the average wave function. (with T. Komorowski, L. Ryzhik),
*Journal of Functional Analysis*,**274**(2018), No. 7, pp. 2113-2138. - Moments of 2D Parabolic Anderson Model. (with W. Xu),
*Asymptotic Analysis*,**108**(2018), No. 3, pp. 151-161. - Heat kernel upper bounds for interacting particle systems. (with A. Giunti, J.-C. Mourrat),
*Annals of Probability*,**47**(2019), No. 2, pp. 1056-1095. - Kardar-Parisi-Zhang equation and large deviations for random walks in weak random environments. (with I. Corwin),
*Journal of Statistical Physics*,**166**(2017), No. 1, pp. 150-168. - High order correctors and two-scale expansions in stochastic homogenization.
*Probability Theory and Related Fields*,**169**(2017), No. 3, pp. 1221-1259. - On generalized Gaussian free fields and stochastic homogenization. (with J.-C. Mourrat),
*Electronic Journal of Probability*,**22**(2017), No. 28, pp. 1-21. - A central limit theorem for fluctuations in 1D stochastic homogenization.
*Stochastics and Partial Differential Equations: Analysis and Computations*,**4**(2016), No. 4, pp. 713-745. - The random Schrödinger equation: slowly decorrelating time-dependent potentials. (with L. Ryzhik),
*Communications in Mathematical Sciences*,**15**(2017), No. 2, pp. 359-378. - The random Schrödinger equation: homogenization in
time-dependent potentials. (with L. Ryzhik),
*Multiscale Modeling and Simulation*,**14**(2016), No. 1, pp. 323-363. - Scaling limit of fluctuations in stochastic homogenization. (with J.-C. Mourrat),
*Multiscale Modeling and Simulation*,**14**(2016), No. 1, pp. 452-481. - Pointwise two-scale expansion for parabolic equations with random coefficients. (with J.-C. Mourrat),
*Probability Theory and Related Fields*,**166**(2016), No. 1, pp. 585-618. - Fluctuations of parabolic equations with large random potentials. (with G. Bal),
*Stochastics and Partial Differential Equations: Analysis and Computations*,**3**(2015), No. 1, pp. 1-51. - Homogenization of parabolic equations with large time-dependent random potential. (with G. Bal),
*Stochastic Processes and their Applications*,**125**(2015), No. 1, pp. 91-115. - Limiting models for equations with large random potential; a review. (with G. Bal),
*Communication in Mathematical Sciences*,**13**(2015), No. 3, pp. 729-748. - Weak convergence approach for parabolic equations with large, highly oscillatory, random potential. (with G. Bal),
*Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques*,**52**(2016), No. 1, pp. 261-285. - An invariance principle for Brownian motion in random scenery. (with G. Bal),
*Electronic Journal of Probability*,**19**(2014), No. 1, pp. 1-19. - Non-local vs local forward equations for option pricing. (with R. Cont), Preprint, 2012.
- Radiative transport limit of Dirac equation with time dependent electromagnetic field. (with G. Bal, O. Pinaud),
*Communications in Partial Differential Equations*,**43**(2018), No. 5, pp. 699-732. - Random homogenization and convergence to integrals with respect to the Rosenblatt process. (with G. Bal),
*Journal of Differential Equations*,**253**(2012), No. 4, pp. 1069-1087. -
Corrector theory for elliptic equations with oscillatory and random potentials with long range correlations. (with G. Bal, J. Garnier and W. Jing),
*Asymptotic Analysis*,**77**(2012), No. 3-4, pp. 123-145.