Yucheng LiuοΌˆεˆ˜ι›¨η¨‹οΌ‰

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.

πŸ“§ 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. Y. Liu. Gaussian deconvolution on ℝd with application to self-repellent Brownian motion. Nov 25, 2024.
    Preprint at arXiv.
  3. M. Dickson and Y. Liu. Decay of connection probability in high-dimensional continuum percolation. Math. Phys. Anal. Geom., 29:21, (2026).
    arXiv
  4. Y. Liu, J. Park and G. Slade. Universal finite-size scaling in high-dimensional critical phenomena. Phys. Rev. E, 113, 024143, (2026).
    arXiv
  5. Y. Liu and G. Slade. Gaussian deconvolution and the lace expansion for spread-out models. Ann. Inst. H. PoincarΓ© Probab. Statist., 62(1): 68--85, (2026).
    pdf
  6. Y. Liu. High-dimensional long-range statistical mechanical models have random walk correlation functions. Electron. J. Probab., 30:192, (2025).
    pdf
  7. Y. Liu and G. Slade. Critical scaling profile for trees and connected subgraphs on the complete graph. Canad. Math. Bull., (2025)
    pdf
  8. 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
  9. Y. Liu, R. Panis and G. Slade. The torus plateau for the high-dimensional Ising model. Commun. Math. Phys., 406:159, (2025).
    arXiv
  10. 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
  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 β„€ 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 β€” UBC Probability seminar
  2. Subcritical two-point functions for high-dimensional statistical mechanical models.
    Nov 12, 2025 β€” Rigorous Statistical Mechanics and Related Topics at Kyoto University
  3. The torus plateau for the high-dimensional Ising model.
    Sept 18, 2025 β€” NYU Shanghai Probability seminar
  4. Decay of two-point functions for high-dimensional statistical mechanical models.
    June 9, 2025 β€” PIMS-CRM Summer School in Probability
  5. The torus plateau for the high-dimensional Ising model.
    Feb 5, 2025 β€” UBC Probability seminar
  6. The torus plateau for the high-dimensional Ising model.
    Dec 1, 2024 β€” CMS Winter Meeting, Discrete Probability session
  7. Continuous-time weakly self-avoiding walk on β„€ has strictly monotone escape speed.
    July 9, 2024 β€” Self-interacting processes at University of Cambridge
    Video
  8. Gaussian deconvolution and the lace expansion.
    Dec 15, 2023 β€” Random Interacting Systems, Scaling Limits, and Universality at National University of Singapore
    Slides
  9. Gaussian deconvolution and the lace expansion.
    Nov 22, 2023 β€” UBC Probability seminar
  10. Continuous-time weakly self-avoiding walk on β„€ has strictly monotone escape speed.
    Oct 25, 2023 β€” SALSIS 2023 at Kyoto University
  11. Continuous-time weakly self-avoiding walk on β„€ has strictly monotone escape speed.
    Sept 21, 2022 β€” UBC Probability seminar

Honours

Teaching Experience