GU, YU 谷雨
 Email: yugull05@gmail.com
 Office Address:
Department of Mathematics, Wean Hall 8212
CMU, Pittsburgh, PA 15213, USA
About me:
I am an assistant professor at CMU. I got my PhD at Columbia in 2014 and did a postdoc at Stanford in 20142017. I was a research member of MSRI in fall 2015.
My general interest is in the study of random dynamics, partial differential equation with random coefficients, and probabilistic models from physics and engineering.
I have been working on stochastic homogenization, wave in random media, and stochastic partial differential equation.
My research has been supported by NSF grant DMS1613301/1807748/1907928 and by the Center for Nonlinear Analysis of CMU.
Teaching at CMU:
 46944 Stochastic Calculus for Finance I, spring 2021.
 21830 Topics in Analysis/Probability, fall 2020.
 21880 Stochastic Calculus, fall 2019, fall 2020.
 21640 Functional Analysis, spring 2019.
 46950 Numerical Methods, fall 2017, fall 2018, fall 2019.
 21366 Stochastic Methods in Applied Mathematics, spring 2018.
I wrote a note on two of my favorite objects  stochastic heat equation and KPZ equation, which can be found here.
Publication:

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. 34, pp. 123145.
 Random homogenization and convergence to integrals with respect to the Rosenblatt process. (with G. Bal),
Journal of Differential Equations, 253 (2012), No. 4, pp. 10691087.
 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. 699732.
 Nonlocal vs local forward equations for option pricing. (with R. Cont),
Preprint, 2012.
 An invariance principle for Brownian motion in random scenery. (with G. Bal), Electronic Journal of Probability, 19 (2014), No. 1, pp. 119.
 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. 261285.
 Limiting models for equations with large random potential; a review. (with G. Bal), Communication in Mathematical Sciences, 13 (2015), No. 3, pp. 729748.
 Homogenization of parabolic equations with large timedependent random potential. (with G. Bal), Stochastic Processes and their Applications, 125 (2015), No. 1, pp. 91115.
 Fluctuations of parabolic equations with large random potentials. (with G. Bal), Stochastics and Partial Differential Equations: Analysis and Computations, 3 (2015), No. 1, pp. 151.
 Pointwise twoscale expansion for parabolic equations with random coefficients. (with J.C. Mourrat), Probability Theory and Related Fields, 166 (2016), No. 1, pp. 585618.
 Scaling limit of fluctuations in stochastic homogenization. (with J.C. Mourrat), Multiscale Modeling and Simulation, 14 (2016), No. 1, pp. 452481.
 The random Schrödinger equation: homogenization in
timedependent potentials. (with L. Ryzhik), Multiscale Modeling and Simulation, 14 (2016), No. 1, pp. 323363.
 The random Schrödinger equation: slowly decorrelating timedependent potentials. (with L. Ryzhik), Communications in Mathematical Sciences, 15 (2017), No. 2, pp. 359378.
 A central limit theorem for fluctuations in 1D stochastic homogenization. Stochastics and Partial Differential Equations: Analysis and Computations, 4 (2016), No. 4, pp. 713745.
 On generalized Gaussian free fields and stochastic homogenization. (with J.C. Mourrat), Electronic Journal of Probability, 22 (2017), No. 28, pp. 121.
 High order correctors and twoscale expansions in stochastic homogenization. Probability Theory and Related Fields, 169 (2017), No. 3, pp. 12211259.
 KardarParisiZhang equation and large deviations for random walks in weak random environments. (with I. Corwin), Journal of Statistical Physics, 166 (2017), No. 1, pp. 150168.
 Heat kernel upper bounds for interacting particle systems. (with A. Giunti, J.C. Mourrat), Annals of Probability, 47 (2019), No. 2, pp. 10561095.
 Moments of 2D Parabolic Anderson Model. (with W. Xu), Asymptotic Analysis, 108 (2018), No. 3, pp. 151161.
 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. 21132138.
 The EdwardsWilkinson 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. 351388.
 Chaos expansion of 2D parabolic Anderson model. (with J. Huang), Electronic Communications in Probability, 23 (2018), No. 26, pp. 110.
 Another look into the WongZakai theorem for stochastic heat equation. (with L.C. Tsai), Annals of Applied Probability, 29 (2019), No. 5, pp. 30373061.
 Fluctuations of random semilinear advection equations. (with T. Komorowski, L. Ryzhik), SIAM Journal on Mathematical Analysis, 50 (2018), No. 5, pp. 52935336.
 The 1D Schrödinger equation with a spacetime white noise: the average wave function. ESAIM: Probability and Statistics, 23 (2019), pp. 338349.
 The random heat equation in dimensions three and higher: the homogenization viewpoint. (with A. Dunlap, L. Ryzhik, O. Zeitouni), to appear in Archive for Rational Mechanics and Analysis, 2021.
 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. 12171258.
 Gaussian fluctuations from the 2D KPZ equation. Stochastics and Partial Differential Equations: Analysis and Computations, 8 (2020), pp. 150185.
 Moments of the 2D SHE at criticality. (with J. Quastel, L.C. Tsai), Probability and Mathematical Physics, 2 (2021), No. 1, pp. 179219.
 Fluctuations of a nonlinear SHE in dimensions three and higher. (with J. Li), SIAM Journal on Mathematical Analysis, 52 (2020), No. 6, pp. 54225440.
 A PDE hierarchy for directed polymers in random environments. (with C. Henderson), Submitted, 2020.
 Gaussian fluctuations from random Schrödinger equation. (with T. Komorowski), Communications in Partial Differential Equations, 46 (2021), No. 2, pp. 201232.
 A forwardbackward SDE from the 2D nonlinear stochastic heat equation. (with A. Dunlap), Submitted, 2020.
 Longtime behavior for a nonlocal model from directed polymers. (with C. Henderson), Submitted, 2020.
 KPZ on torus: Gaussian fluctuations. (with T. Komorowski), Submitted, 2021.
 A quenched local limit theorem for stochastic flows. (with A. Dunlap), Submitted, 2021.