Le Chen

Visiting assistant professor

Emory University
Department of Mathematics
400 Dowman Drive
Atlanta, GA 30322 USA
Email: le.chen AT emory.edu (Internet)
Tel: +1 404 727 5641
FAX: +1 404 727 5611

About me

I am a visiting assistant professor at Emory University. Before this, I was a tenure-track assistant professor at the University of Nevada, Las Vegas, from 2018-2019 for three semesters and the Black-Babcock visiting assistant professor at the University of Kansas from 2015-2017 for five semesters. I obtained my Ph.D. in April 2013 from Swiss Federal Institute of Technology, Lausanne -- École Polytechnique Fédérale de Lausanne. In 2014, I obtained an SNSF (Swiss National Science Foundation) post-doctoral research fellowship to spend one year at the University of Utah. I am an analysist/probabilist, working on stochastic analysis and stochastic partial differential equations.

You may find more information in my Curriculum Vitae.
We will host the Frontier Probability Days '21 at UNLV, which was postponed from May 8-10, 2020 to May 16-18, 2020 due to the Covid-19.

Teaching

Publications

Submitted or under preparation

  1. (with N. Eisenberg) Fractional SPDE with time-independent noise: solvability and exact asymptotics (37 pages)

  2. (with G. Hu) Hölder regularity of the nonlinear stochastic time-fractional slow and fast diffusion equations on Rd. arXiv:2105.00891 (17 pages)

  3. (with D. Khoshnevisan, D. Nualart, and F. Pu) Central limit theorems for spatial averages of the stochastic heat equation via Malliavin-Stein's method. arXiv:2008.02408 (43 pages)

  4. (with D. Khoshnevisan, D. Nualart, and F. Pu) Spatial ergodicity for SPDEs via a Poincaré-inequalities. arXiv:1907.11553 (40 pages)

  5. (with J. Huang) Regularity and strict positivity of densities for the stochastic heat equation on Rd. arXiv:1902.02382 (94 pages)

Published (or to appear)

  1. (with D. Khoshnevisan, D. Nualart, and F. Pu) A CLT for dependent random variables, with applications to infinitely-many interacting diffusion processes.
    Proceedings of American Mathematical Society,     to appear, 2021.

  2. (with D. Khoshnevisan, D. Nualart, and F. Pu) Poincaré-inequalities, and central limit theorems for parabolic stochastic partial differential equations.
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques,     to appear, 2021.

  3. (with D. Khoshnevisan, D. Nualart, and F. Pu) Spatial ergodicity and central limit theorems for parabolic Anderson model with delta initial conditions.
    Journal of Functional Analysis,     pending revision, 2021.

  4. (with R. Balan and X. Chen) Exact asymptotics of the stochastic wave equation with time-independent noise.
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques,     accepted pending revision, 2021.

  5. (with K. Kim) Stochastic comparison for stochastic heat equation on Rd.
    Electronic Journal of Probability,     25, article No. 140, 1--38, 2020.

  6. (with J. Huang, D. Khoshnevisan and K. Kim) Dense blowup for parabolic SPDEs.
    Electronic Journal of Probability, Vol. 24, paper no. 118, 1-33, 2019.

  7. (with Y. Hu and D. Nualart) Nonlinear stochastic time-fractional slow and fast diffusion equations on Rd.
    Stochastic Processes and their Applications, 129, 5073-5112, 2019.

  8. (with Y. Hu and D. Nualart) Regularity and strict positivity of densities for the nonlinear stochastic heat equation.
    Memoirs of American Mathematical Society, accepted in 2018, estimated to appear in mid-2021 due to long backlog ,arXiv:1611.03909.

  9. (with J. Huang) Comparison principle for stochastic heat equation on Rd.
    Annals of Probability, Vol. 47, No. 2, 989-1035, 2019.

  10. (with K. Kim) Nonlinear stochastic heat equation driven by spatially colored noise: moments and intermittency.
    Acta Mathematica Scientia, 39B (3): 645-668, 2019.

  11. (with Y. Hu, K. Kalbasi and D. Nualart) Intermittency for the stochastic heat equation driven by a rough time fractional Gaussian noise.
    Probability Theory and Related Fields, 171(1), 431-457, 2018.

  12. (with R. Balan) Parabolic Anderson Model with space-time homogeneous Gaussian noise and rough initial condition.
    Journal of Theoretical Probability, 31 (4), 2216-2265, 2018.

  13. (with Y. Hu and D. Nualart) Two-point correlation function and Feynman-Kac formula for the stochastic heat equation.
    Potential Analysis, 46 (4), 779-797, 2017.

  14. (with K. Kim) On comparison principle and strict positivity of solutions to the nonlinear stochastic fractional heat equations.
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 53 (1), 358-388, 2017.

  15. (with M. Cranston, D. Khoshnevisan and K. Kim) Dissipation and high disorder.
    Annals of Probability, 45 (1), 82-99, 2017.

  16. (with D. Khoshnevisan and K. Kim) A boundedness trichotomy for the stochastic heat equation.
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 53 (4), 1991-2004, 2017.

  17. Nonlinear stochastic time-fractional diffusion equations on R: moments, Hölder regularity and intermittency.
    Transactions of the American Mathematical Society, 369 (12), 8497-8535, 2017.

  18. (with G. Hu, Y. Hu and J. Huang) Space-time fractional diffusions in Gaussian noisy environment.
    Stochastics, 89 (1), 171-206, 2016.

  19. (with D. Khoshnevisan and K. Kim) Decorrelation of total mass via energy.
    Potential Analysis, 45 (1). 157-166, 2016.

  20. (with R. Dalang) Moment bounds and asymptotics for the stochastic wave equation.
    Stochastic Processes and their Applications, 125 (4), 1605-1628, 2015.
    (This paper corresponds mostly to Section 3 of the unpublished notes arXiv:1401.6506v1)

  21. (with R. Dalang) Moments, intermittency and growth indices for nonlinear stochastic fractional heat equation.
    Stochastic Partial Differential Equations: Analysis and Computations, 3 (3), 360-397, 2015.

  22. (with R. Dalang), Moments and growth indices for the nonlinear stochastic heat equation with rough initial conditions.
    Annals of Probability, 43 (6), 3006-3051, 2015.

  23. (with R. Dalang) Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions.
    Stochastic Partial Differential Equations: Analysis and Computations, 2 (3), 316-352, 2014.

Ph.D. thesis

  1. Moments, intermittencey, and growth indices for nonlinear stochastic PDE's with rough initial conditions.
    École polytechnique fédérale de Lausanne, Thesis No. 5712 , 2013.

Some unpublished preprints

My math coauthors

Balan, Raluca University of Ottawa, CA 2
Chen, Xia University of Tennessee 1
Cranston, Michael University of California, Irvine 1
Dalang, Robert École Polytechnique Fédérale de Lausanne, Switzerland 4
Eisenberg, Nicholas (Ph.D. candidate) University of Nevada, Las Vegas/Auburn University 1
Hu, Guannan Washburn University 2
Hu, Yaozhong University of Alberta, CA 5
Huang, Jingyu University of Birmingham, UK 4
Kalbasi, Kamran University College Dublin 1
Khoshnevisan, Davar University of Utah 9
Kim, Kunwoo Pohang University of Science and Technology, Korea 7
Nualart, David University of Kansas 9
Pu, Fei University of Luxembourg, Luxembourg 5

Previous work on computer science

Research interests:

Statistical machine learning, probabilistic graphical model, time series, mixture model, content-based image retrieval, computer vision, etc.

US patent

Publications

  1. L. Chen, D. Barber and J. Odobe. Dynamical Dirichlet mixture model, IDIAP-RR, 2007. Source code available here.
  2. L. Chen, L. Zhang, F. Jing, K. Deng and W.-Y. Ma. Ranking web objects from multiple communities. ACM 14th Conference on Information and Knowledge Management (CIKM), 2006, 377-386.
  3. L. Zhang, L. Chen, F. Jing, K. Deng and W.-Y. Ma. EnjoyPhoto: a vertical image search engine for enjoying high-quality photos. ACM Multimedia, 2006.
  4. X. Li, L. Chen, L. Zhang, F. Lin and W.-Y. Ma. Image annotation by large-scale content-based image retrieval. ACM Multimedia, 2006.
  5. D. Wang, D. Ding, L. Chen, S. Zhang, F. Lin, B. Zhang. Two kinds of timing cues and their usage in concept detection in news video, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2005.
  6. L. Chen, D. Ding, D. Wang, F. Lin and B. Zhang. AP-based Borda voting method for feature extraction in trecvid-2004. In: Losada D.E., Fernandez-Luna J.M. (eds) Advances in Information Retrieval. ECIR 2005. Lecture Notes in Computer Science, vol 3408. Springer, Berlin, Heidelberg, 2005.
  7. D. Ding, L. Chen, B. Zhang. Temporal shot clustering analysis for video concept detection. In: Losada D.E., Fernandez-Luna J.M. (eds) Advances in Information Retrieval. ECIR 2005. Lecture Notes in Computer Science, vol 3408. Springer, Berlin, Heidelberg, 2005.
© Le Chen, 2019, Emory