GU, YU 谷雨
- Email: yg1 AT stanford DOT edu
- Office Address:
Department of Mathematics, Office 382C
Building 380, Stanford University
Stanford, CA 94305, USA
- Szegö Assistant Professor, Stanford University, 2014 - present
- Ph.D. Applied Mathematics, Columbia University, 2010 - 2014
- M.S. Applied Mathematics, Brown University, 2009 - 2010
- B.S. Mathematics and Physics, Tsinghua University, China, 2005 - 2009
My research interest lies in the general areas of partial differential equations and probability, in particular, stochastic homogenization, wave propagation in random media, SPDE, probabilistic methods in mathematical physics. I was a research member of MSRI in fall 2015. My research is supported by NSF grant DMS-1613301.
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.
- 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.
- Radiative transport limit of Dirac equation with time dependent electromagnetic field. (with G. Bal), Preprint, 2012.
- Non-local vs local forward equations for option pricing. (with R. Cont),
- An invariance principle for Brownian motion in random scenery. (with G. Bal), Electronic Journal of Probability, 19 (2014), No. 1, pp. 1-19.
- 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.
- Limiting models for equations with large random potential; a review. (with G. Bal), Communication in Mathematical Sciences, 13 (2015), No. 3, pp. 729-748.
- 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.
- Fluctuations of parabolic equations with large random potentials. (with G. Bal), Stochastic Partial Differential Equations: Analysis and Computations, 3 (2015), No. 1, pp. 1-51.
- 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.
- Scaling limit of fluctuations in stochastic homogenization. (with J.-C. Mourrat), Multiscale Modeling and Simulation, 14 (2016), No. 1, pp. 452-481.
- The random Schrödinger equation: homogenization in
time-dependent potentials. (with L. Ryzhik), Multiscale Modeling and Simulation, 14 (2016), No. 1, pp. 323-363.
- The random Schrödinger equation: slowly decorrelating time-dependent potentials. (with L. Ryzhik), Communications in Mathematical Sciences, 15 (2017), No. 2, pp. 359-378.
- A central limit theorem for fluctuations in 1D stochastic homogenization. Stochastic Partial Differential Equations: Analysis and Computations, 4 (2016), No. 4, pp. 713-745.
- On generalized Gaussian free fields and stochastic homogenization. (with J.-C. Mourrat), Electronic Journal of Probability, 22 (2017), No. 28, pp. 1-21.
- High order correctors and two-scale expansions in stochastic homogenization. to appear in Probability Theory and Related Fields, 2016.
- 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.
- Heat kernel upper bounds for interacting particle systems. (with A. Giunti, J.-C. Mourrat), Submitted, 2016.
- Moments of 2D Parabolic Anderson Model. (with W. Xu), Submitted, 2017.
- The Schrödinger equation with spatial white noise: the average wave function. (with T. Komorowski, L. Ryzhik), Submitted, 2017.