Xuda Ye

PhD Thesis

Ergodicity and Long-Time Error of Complicated Stochastic Processes and Numerical Methods (2025)

Publications

1. Xuda Ye & Zhennan Zhou (2021)
   Efficient sampling of thermal averages of interacting quantum particle systems with random batches
   The Journal of Chemical Physics, 154(20)
   https://doi.org/10.1063/5.0047437 [pdf]
2. Shi Jin, Lei Li, Xuda Ye & Zhennan Zhou (2023)
   Ergodicity and long-time behavior of the Random Batch Method for interacting particle systems
   Mathematical Models and Methods in Applied Sciences, 33 (01), 67-102
   https://doi.org/10.1142/S0218202523500033 [pdf]
3. Xuda Ye, & Zhennan Zhou (2023)
   Error analysis of time-discrete Random Batch Method for interacting particle systems and associated mean-field limits
   IMA Journal of Numerical Analysis, drad043
   https://doi.org/10.1093/imanum/drad043 [pdf]
4. Xuda Ye, & Zhennan Zhou (2025)
   Dimension-free ergodicity of path integral molecular dynamics
   Communications in Computational Physics, 38(5), 1355-1388
   https://doi.org/10.4208/cicp.OA-2024-0004 [pdf]
5. Xuda Ye, & Zhennan Zhou (2025)
   Optimal convergence rate of Lie–Trotter approximation for quantum thermal averages
   arXiv preprint: 2309.05188 (accepted by SIAM Journal on Mathematical Analysis)
   https://arxiv.org/abs/2309.05188
6. Jianfeng Lu, Xuda Ye, & Zhennan Zhou (2025)
   Mean square error analysis of stochastic gradient and variance-reduced sampling algorithms
   arXiv preprint: 2511.04413
   https://arxiv.org/abs/2511.04413
7. Qi Feng, Rongjie Lai, Di Qi, & Xuda Ye (2026) [new]
   Mode coverage in normalizing flow Boltzmann generators via log-ratio variation 
   arXiv preprint: 2609.09473
   https://arxiv.org/abs/2609.09473 [slides]
   Code: https://github.com/xuda-ye-math/KLXX
8. Xuda Ye (2026) [new]
   Mean square error analysis of stochastic Runge–Kutta integrators
   arXiv preprint: 2609.11528
   https://arxiv.org/abs/2609.11528 [pdf] [slides]
   Code: https://github.com/xuda-ye-math/Poisson-Overdamped
9. Yuliang Wang, & Xuda Ye (2026) [new]
   A sharp uniform-in-time Wasserstein-1 bound for stochastic Runge–Kutta integrators of Langevin dynamics
   ai.viXra preprint: 2609.0049
   https://ai.vixra.org/abs/2609.0049 [pdf]
10. Xuda Ye (2026)
    Classification of the orbits of three quadratic Collatz-type maps
    arXiv preprint: 2610.10660
    https://arxiv.org/abs/2610.10660 [pdf]
    Code: https://github.com/xuda-ye-math/Collatz
11. Xuda Ye, & Yuliang Wang (2026) [new]
    Stochastic gradient Leimkuhler–Matthews integrator with second order discretization error
    ai.viXra preprint: 2610.0030
    https://ai.vixra.org/abs/2610.0030