Yucheng Liu（刘雨程）

I am a postdoc fellow in the Beijing International Center for Mathematical Research at Peking University, hosted by Jian Ding. I did my Ph.D. at the University of British Columbia, under the supervision of Gordon Slade.

📧 yliu135@pku.edu.cn
ORCID: 0000-0002-1917-8330

Research Interests

Preprints & Publications

  1. Y. Liu and G. Slade. Crossover from subcritical to critical decay: random walk, self-avoiding walk, percolation. May 15, 2026.
    Preprint at arXiv
  2. M. Dickson and Y. Liu. Decay of connection probability in high-dimensional continuum percolation. Math. Phys. Anal. Geom., 29: 21, (2026).
    arXiv
  3. Y. Liu. Gaussian deconvolution on ℝd with application to self-repellent Brownian motion. J. Funct. Anal., 291(7): 111579, (2026).
    arXiv
  4. Y. Liu. High-dimensional long-range statistical mechanical models have random walk correlation functions. Electron. J. Probab., 30: 192, (2025).
    pdf
  5. Y. Liu, J. Park and G. Slade. Universal finite-size scaling in high-dimensional critical phenomena. Phys. Rev. E, 113: 024143, (2026).
    arXiv
  6. Y. Liu and G. Slade. Critical scaling profile for trees and connected subgraphs on the complete graph. Canad. Math. Bull., 69(2): 550-565, (2026).
    pdf
  7. Y. Liu and G. Slade. Near-critical and finite-size scaling for high-dimensional lattice trees and animals. J. Stat. Phys., 192: 32, (2025).
    arXiv
  8. Y. Liu, R. Panis and G. Slade. The torus plateau for the high-dimensional Ising model. Commun. Math. Phys., 406: 159, (2025).
    arXiv
  9. Y. Liu. A general approach to massive upper bound for two-point function with application to self-avoiding walk torus plateau. Electron. J. Probab., 30: 110, (2025).
    pdf
  10. Y. Liu and G. Slade. Gaussian deconvolution and the lace expansion for spread-out models. Ann. Inst. H. Poincaré Probab. Statist., 62(1): 68-85, (2026).
    pdf
  11. Y. Liu and G. Slade. Gaussian deconvolution and the lace expansion. Probab. Theory Relat. Fields, (2024).
    arXiv
  12. Y. Liu. Continuous-time weakly self-avoiding walk on ℤ has strictly monotone escape speed. Ann. Appl. Probab., 34(6): 5522-5555, (2024).
    pdf video

Invited Talks

  1. Subcritical two-point functions for high-dimensional statistical mechanical models.
    Nov 26, 2025 — UBC Probability seminar
  2. Subcritical two-point functions for high-dimensional statistical mechanical models.
    Nov 12, 2025 — Rigorous Statistical Mechanics and Related Topics at Kyoto University
  3. The torus plateau for the high-dimensional Ising model.
    Sept 18, 2025 — NYU Shanghai Probability seminar
  4. Decay of two-point functions for high-dimensional statistical mechanical models.
    June 9, 2025 — PIMS-CRM Summer School in Probability
  5. The torus plateau for the high-dimensional Ising model.
    Feb 5, 2025 — UBC Probability seminar
  6. The torus plateau for the high-dimensional Ising model.
    Dec 1, 2024 — CMS Winter Meeting, Discrete Probability session
  7. Continuous-time weakly self-avoiding walk on ℤ has strictly monotone escape speed.
    July 9, 2024 — Self-interacting processes at University of Cambridge
    Video
  8. Gaussian deconvolution and the lace expansion.
    Dec 15, 2023 — Random Interacting Systems, Scaling Limits, and Universality at National University of Singapore
    Slides
  9. Gaussian deconvolution and the lace expansion.
    Nov 22, 2023 — UBC Probability seminar
  10. Continuous-time weakly self-avoiding walk on ℤ has strictly monotone escape speed.
    Oct 25, 2023 — SALSIS 2023 at Kyoto University
  11. Continuous-time weakly self-avoiding walk on ℤ has strictly monotone escape speed.
    Sept 21, 2022 — UBC Probability seminar

Honours

Teaching Experience