Research

  1. Submitted
    On discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator
    Ziran Liu and Chung Pang Mok
    Submitted for Publication, 2026
    arXiv PDF
  2. Preprint
    Nonexistence of vanishing-viscosity limits for mechanical Hamiltonian ergodic problems
    Ziran Liu, Hung V. Tran, and Yifeng Yu
    Preprint, 2026
    arXiv PDF
  3. Submitted
    Sharp global and almost everywhere convergence rates for periodic homogenization of viscous quadratic Hamilton-Jacobi equations
    Ziran Liu, Hung V. Tran, and Yifeng Yu
    Submitted for Publication, 2026
    arXiv PDF
  4. Submitted
    Geometric and Spectral Alignment for Deep Neural Network II
    Ziran Liu, Wei Wang, Jinhao Wang, Pengcheng Wang, Xinyi Sui, Cihan Ruan, Nam Ling, and Wei Jiang
    Submitted for Publication, 2026
    arXiv PDF
  5. Submitted
    Geometric and Spectral Alignment for Deep Neural Network I
    Ziran Liu, Wei Wang, Jinhao Wang, Pengcheng Wang, Xinyi Sui, Cihan Ruan, Nam Ling, and Wei Jiang
    Submitted for Publication, 2026
    arXiv PDF
  6. Preprint
    Joint thick-point content for log-correlated fields
    Ziran Liu
    Preprint, 2026
    PDF
  7. Submitted
    Joint Multifractal Spectra for Correlated Gaussian Multiplicative Chaos and an Application to Circular β-Ensembles
    Ziran Liu
    Submitted for Publication, 2026
    PDF
  8. Preprint
    Information-Constrained Prophet Inequalities via Kolmogorov-Wiener Prediction Theory
    Ziran Liu
    Preprint, 2026
    PDF
  9. Submitted
    Gaussian Chaos Noise: Variational Noise Design for Reliable Deep Learning
    Ziran Liu
    Submitted for Publication, 2026
    PDF
  10. WIP
    APS Spectral Flow for Selective Propagation in Geometric Deep Learning
    Ziran Liu
    Working Manuscript, 2025
    PDF
  11. Preprint
    State-Dimension Laws for Prediction: Hankel Geometry of Finite-Memory Predictors
    Ziran Liu
    Preprint, 2025
    PDF
  12. Preprint
    On Ruckle’s conjecture for one-stage accumulation games: a coupling lift and a proved regime
    Ziran Liu
    Preprint, 2025
    PDF
  13. Preprint
    Variational Kernel Design for Internal Noise: GCh Noise and Representation Compatibility in Deep Learning
    Ziran Liu
    Preprint, 2025
    PDF
  14. Submitted
    Approaching the Prescribed Gaussian Curvature by Discrete Conformality
    Ziran Liu and Tianqi Wu
    Submitted for Publication, 2024
    arXiv PDF
  15. Article
    Reflected Brownian Motion with Drift in a Wedge
    Peter Lakner, Ziran Liu, and Josh Reed
    Queueing Systems, 2023
    Bib PDF
  16. Preprint
    A Lichnerowicz Vanishing Theorem for Proper Cocompact Actions
    Ziran Liu
    Preprint, 2013
    arXiv PDF
  17. Thesis
    Reflected Brownian Motion and its Applications to Differential Geometry and Index Theory
    Ziran Liu
    May 2023
    PDF
  18. Thesis
    Stationary Gaussian Processes and the Kolmogorov-Wiener Prediction Problem
    Ziran Liu
    May 2016
    PDF
  19. Thesis
    Lichnerowicz Type Vanishing Theorem for Mathai-Zhang Index
    Ziran Liu
    Jun 2014
    PDF