My primary research field is probability. More specifically, I am interested in ergodic properties of SPDEs and models related to the Kardar–Parisi–Zhang universality class, including stochastic Burgers/Hamilton–Jacobi equations, directed polymers, first-/last-passage percolation, etc.

Papers

Probability

  • Khanin Konstantin, L. Li, On the rate of convergence to coalescing Brownian motions, https://arxiv.org/abs/2110.09731, Ann. Inst. H. Poincaré Probab. Statist. 60(1): 208-231 (2024)
  • Alexander Dunlap, Yu Gu, L. Li, Localization length of the 1+1 continuum directed random polymer, https://arxiv.org/abs/2211.07318, Annales Henri Poincaré, volume 24, pages 2537–2555 (2023)
  • Khanin Konstantin, L. Li, Zhanghan Yin, Point fields of last-passage percolation and coalescing fractional Brownian motions, https://arxiv.org/abs/2112.02247, Phys. Rev. E 105, 064127
  • Khanin Konstantin, L. Li, On end-point distribution for directed polymers and related problems for random forced Burgers equation, Phil. Trans. R. Soc. A. 380: 20210081
  • Yuri Bakhtin, L. Li, Strongly mixing smooth planer vector field without asymptotic directions, https://arxiv.org/abs/1903.02733, Nonlinearity 36 1789 (2023)
  • Yuri Bakhtin, L. Li, Weakly mixing smooth planer vector field without asymptotic directions, https://arxiv.org/abs/1808.05544, Proc. Amer. Math. Soc., 148 (2020), 4733-4744
  • Yuri Bakhtin, L. Li, Zero temperature limit for directed polymers and inviscid limit for stationary solutions of stochastic Burgers equation, https://arxiv.org/abs/1706.09950, J. Stat. Phys. 172, 1358-1397 (2018)
  • Yuri Bakhtin, L. Li, Thermodynamic limit for directed polymers and stationary solutions of the Burgers equation, https://arxiv.org/abs/1607.04864, Comm. Pure Appl. Math., 72(3), (2019), 536-619

Applied math

  • Alan E. Rask, L. Li, and Paul M. Zimmerman, Kohn–Sham Density in a Slater Orbital Basis Set, J. Phys. Chem. A, 128, 16, 3194–3204 (2024)
  • Zhiyi You, L. Li, Jianfeng Lu, Hao Ge, Integrated tempering enhanced sampling method as the infinite switching limit, https://arxiv.org/abs/1806.00725, J. Chem. Phys., 149, 084114 (2018)

Thesis

  • Ph.D. Thesis (advisor: Yuri Bakhtin), Ergodic problems in random environments: polymers, Burgers equation and transport, 2019, New York University (pdf)
  • Undergraduate Thesis (advisor: Hao Ge 葛颢), Enhanced Sampling method, 2014, Peking University