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Le Chen

Tenure-track Assistant Professor
Auburn University
Department of Mathematics and Statistics
203 Parker Hall
Auburn, Alabama 36849
Email: le.chen AT auburn.edu
Zoom: 8141875411

About Me

I am a tenure-track assistant professor at Auburn University. Prior to this role, I held a position as a visiting assistant professor at Emory University from 2019-2021, spanning four semesters. From 2018-2019, I was a tenure-track assistant professor at the University of Nevada, Las Vegas, for three semesters. Earlier in my career, I held the Black-Babcock visiting assistant professorship at the University of Kansas working closely with David Nualart and Yaozhong Hu, a role I fulfilled from 2015-2017 over the course of five semesters.

My academic journey began at the Swiss Federal Institute of Technology, Lausanne -- École Polytechnique Fédérale de Lausanne, where I obtained my Ph.D. in April 2013 under the supervision of Robert Dalang. Following this, I received an SNSF (Swiss National Science Foundation) post-doctoral research fellowship in 2014, which allowed me to spend a year at the University of Utah working with Davar Khoshnevisan.

My research focus lies within the fields of analysis and probability, specifically working on stochastic analysis and stochastic partial differential equations.

Funding Supports

Conferences or Seminars

Teaching

Course code Course Year Term University
Math 7830 Stochastic processes II 2024 Spring Auburn
Math 7820 Stochastic processes I 2023 Fall
Math 7810 Probability II (Measure-based) Spring
Math 7010 Applied Mathematics II
Math 7800 Probability I (Measure-based) 2022 Fall
Math 7000 Applied Mathematics I
Math 7210 Real Analysis II Spring
Math 5870/6870 Mathematical Finance 2021 Fall
STAT 3600 Probability & Statistics - I
Summer Boost Camp For Bioinformatics Ph.D. program Summer Emory
Math 362 Mathematical Statistics - II Spring
Math 221 (two sessions) Linear Algebra
Math 221 (three sessions) 2020 Fall
Math 362 (two sessions) Mathematical Statistics - II Spring
Math 361 (two sessions) Mathematical Statistics - I 2019 Fall
Math 463/663 Advanced Matrix Theory Spring UNLV
Math 283 Calculus III
Math 432 Elementary Complex Analysis 2018 Fall
Math 181 Calculus I
Math 365 Computational Linear Algebra Spring
Math 526 Probability and Statistics 2017 KU
Math 526 2016 Fall
Math 526 Spring
Math 526 2015 Fall
Math 526 Spring

Publications

Submitted or under preparation

Pdf Co-authors Title Ref Misc
36 M. Foondun, J. Huang, and M. Salins Global solution for superlinear stochastic heat equation on Rd under Osgood-type conditions arXiv:2310.02153 22 pages
35 C. Ouyang and W. Vickery Parabolic Anderson model with colored noise on torus arXiv:2308.10802 30 pages
34 P. Xia Asymptotic properties of stochastic partial differential equations in the sublinear regime arXiv:2306.06761 50 pages

Published or to appear

Pdf Co-authors Title Journal Year Status
33 S. Kuzgun, C. Mueller, and P. Xia On the radius of the self-repellent fractional Brownian motion Journal of Statistical Physics 2023 Accepted, pending revision
32 N. Eisenberg Invariant measures for the nonlinear stochastic heat equation on Rd without any drift term Journal of Theoretical Probability To appear
31 Y. Guo and J. Song Moments and asymptotics for a class of SPDEs with space-time white noise Transactions of the American Mathematical Society Accepted, pending revision
30 D. Candil and C.Y. Lee Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds Stochastic Partial Differential Equations: Analysis and Computations To appear
29 N. Eisenberg Interpolating the stochastic heat and wave equations with time-independent noise: solvability and exact asymptotics 11 (3):1203-1253
28 J. Huang Superlinear stochastic heat equation on Rd Proceedings of American Mathematical Society 151 (9):4063-4078
27 D. Khoshnevisan, D. Nualart, and F. Pu Central limit theorems for spatial averages of the stochastic heat equation via Malliavin-Stein's method Stochastic Partial Differential Equations: Analysis and Computations 11 (1):122-176
26 R. Balan and Y. Ma Parabolic Anderson model with rough noise in space and general initial conditions Electronic Communication of Probability 2022 (2022) Paper No. 65, 12 pp.
25 G. Hu Hölder regularity of the nonlinear stochastic time-fractional slow and fast diffusion equations on Rd Fractional Calculus and Applied Analysis 25 (2), 608-629.
24 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 282 (2), Paper No. 109290, 35 pp.
23 Spatial ergodicity for SPDEs via a Poincaré-inequalities Electronic Journal of Probability 2021 26, Paper No. 140, 37 pp.
22 A CLT for dependent random variables, with applications to infinitely-many interacting diffusion processes. Proceedings of American Mathematical Society 149 (12), 5367–5384
21 Central limit theorems for parabolic stochastic partial differential equations. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 58 (2), 1052-1077
20 R. Balan and X. Chen Exact asymptotics of the stochastic wave equation with time-independent noise. 58 (2022), no. 3, 1590-1620
19 Y. Hu and D. Nualart Regularity and strict positivity of densities for the nonlinear stochastic heat equation. Memoirs of American Mathematical Society Vol. 273, no. 1340.
18 K. Kim Stochastic comparison for stochastic heat equation on Rd. Electronic Journal of Probability 2020 25, article No. 140, 1--38
17 J. Huang, D. Khoshnevisan and K. Kim Dense blowup for parabolic SPDEs. 2019 Vol. 24, paper no. 118, 1-33
16 Y. Hu and D. Nualart Nonlinear stochastic time-fractional slow and fast diffusion equations on Rd. Stochastic Processes and their Applications 129, 5073-5112
15 J. Huang Comparison principle for stochastic heat equation on Rd. Annals of Probability Vol. 47, No. 2, 989-1035
14 K. Kim Nonlinear stochastic heat equation driven by spatially colored noise: moments and intermittency. Acta Mathematica Scientia 2018 39B (3): 645-668
13 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
12 R. Balan Parabolic Anderson Model with space-time homogeneous Gaussian noise and rough initial condition. Journal of Theoretical Probability 31 (4), 2216-2265
11 Y. Hu and D. Nualart Two-point correlation function and Feynman-Kac formula for the stochastic heat equation Potential Analysis 2017 46 (4), 779-797
10 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
9 M. Cranston, D. Khoshnevisan and K. Kim Dissipation and high disorder Annals of Probability 45 (1), 82-99
8 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
7   Nonlinear stochastic time-fractional diffusion equations on R: moments, Hölder regularity and intermittency Transactions of the American Mathematical Society 369 (12), 8497-8535
6 G. Hu, Y. Hu and J. Huang Space-time fractional diffusions in Gaussian noisy environment Stochastics 89 (1), 171-206
5 D. Khoshnevisan and K. Kim Decorrelation of total mass via energy. Potential Analysis 2016 45 (1), 157-166
4 \(^*\) R. Dalang Moment bounds and asymptotics for the stochastic wave equation Stochastic Processes and their Applications 2015 125 (4), 1605-1628
3 Moments, intermittency and growth indices for nonlinear stochastic fractional heat equation Stochastic Partial Differential Equations: Analysis and Computations 3 (3), 360-397
2 Moments and growth indices for the nonlinear stochastic heat equation with rough initial conditions Annals of Probability 43 (6), 3006-3051
1 Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions Stochastic Partial Differential Equations: Analysis and Computations 2014 2 (3), 316-352

\(^*\) This paper corresponds mostly to Section 3 of the unpublished notes [-2] arXiv:1401.6506v1

Ph.D. thesis

Pdf Adviser Title Year Misc
0 Robert C. Dalang Moments, intermittencey, and growth indices for nonlinear stochastic PDE's with rough initial conditions. 2013 The École polytechnique fédérale de Lausanne, Thesis No. 5712

Some unpublished notes

Pdf Co-authors Title Year Misc
-1 R. Dalang The nonlinear stochastic heat equation with rough initial data: a summary of some new results 2012 arXiv:120.1690
-2 Moment bounds in spde's with application to the stochastic wave equation 2014 arXiv:1401.6506
-3   The third moment for the parabolic Anderson model 2016 arXiv:1609.01005
-4 J. Huang Regularity and strict positivity of densities for the stochastic heat equation on Rd 2019 arXiv:1902.02382

Journal Counts

Journal Counts
Stochastic Partial Differential Equations: Analysis and Computations 5
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 4
Annals of Probability 3
Electronic Journal of Probability 3
Journal of Theoretical Probability 2
Potential Analysis 2
Proceedings of American Mathematical Society 2
Stochastic Processes and their Applications 2
Transactions of the American Mathematical Society 2
Acta Mathematica Scientia 1
Electronic Communication of Probability 1
Fractional Calculus and Applied Analysis 1
Journal of Functional Analysis 1
Journal of Statistical Physics 1
Memoirs of American Mathematical Society 1
Probability Theory and Related Fields 1
Stochastics 1
Total 33

Math Coauthors

Name University Counts
Balan, Raluca University of Ottawa, CA 3
Chen, Xia University of Tennessee 1
Candil, David École Polytechnique Fédérale de Lausanne, Switzerland 1
Cranston, Michael University of California, Irvine 1
Dalang, Robert École Polytechnique Fédérale de Lausanne, Switzerland 4
Eisenberg, Nicholas University of Nevada, Las Vegas/Auburn University 2
Foondun, Mohammud University of Strathclyde, Glasgow, UK 1
Guo, Yuhui Shandong University, CN 1
Hu, Guannan Washburn University 2
Hu, Yaozhong University of Alberta, CA 5
Huang, Jingyu University of Birmingham, UK 6
Kalbasi, Kamran University College Dublin 1
Khoshnevisan, Davar University of Utah 9
Kim, Kunwoo Pohang University of Science and Technology, Korea 7
Kuzgun, Sefika University of Rochester 1
Lee, Cheuk Yin Taiwan Tsing Hua University 1
Ma, Yiping University of Ottawa, CA 1
Mueller, Carl University of Rochester 1
Nualart, David University of Kansas 9
Ouyang, Cheng University of Illinois, Chicago 1
Pu, Fei Beijing Normal University 5
Salins, Mickey Boston University 1
Song, Jian Shandong University, CN 1
Vickery, William University of Illinois, Chicago 1
Xia, Panqiu Auburn University 2

Supervision of Ph.D. Students and Postdocs

Ph.D. Students

Postdocs

Name Years
Xia, Panqiu 2022 Fall -- Now

Outreach

  1. Auburn University Summer Science Institute (AU-SSI)
  2. Destination STEM (official website)
  3. Graduate Student Seminars (Github)
    1. 2021-09-27: Introduction to stochastic partial differential equations
    2. 2023-01-18: Introduction to stochastic heat equation
    3. 2023-02-15: Sharpening your saw before cutting down the tree -- Personal development environment (PDE)
    4. 2023-11-01: Disorderly surface growth

Open source projects

GitHub Projects Descriptions Teaching/Education Research Software Citation/Documentations
chenle02/SPDEs-Bib SPDEs-Bib: A Comprehensive Bibliography of Stochastic Partial Differential Equations and Related Topics   X  
chenle02/Fox-H_Symbolic_Tools Some symbolic tools for the Fox H-function   X X
chenle02/Open_Slides_for_Linear_Algebra Open slides for linear algebra X    
chenle02/Open_Slides_Statistics Statistics: Open Slides X    
chenle02/2022_SSI-AU_Probability_by_Le Probability: Summer Science Institute at Auburn X    
chenle02/NSF-Awards Awards from National Science Foundation (NSF) with a Focus on Division of Mathematical Sciences (DMS)   X  
chenle02/Graduate_Student_Seminars_by_Le_Chen Graduate Student Seminars by Le Chen X    
chenle02/Open_Slides_Financial_Mathematics Financial Mathematics: Open Slides X    
chenle02/Simulations_on_Some_Surface_Growth_Models This is a python package to simulate the surface growth using, e.g, Tetris pieces. X X X Documentations in html and pdf

Miscs

Social Medias in Academia Others
Google Scholar arXiv Github Huggingface
ORCID Research Gate Tereminal Cast Twitwer/X
Mathscinet Linkedin My neovim 0.5+ setup  
Web of Science (Publon)