GU, YU   谷雨

• 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.