Yucheng Liu

I am a 4th year PhD student in the Mathematics department at the University of British Columbia. I am in the Probability Group and my supervisor is Gordon Slade.

Email: yliu135@math.ubc.ca
Address: #121-1984 Mathematics Rd, Vancouver, BC V6T 1Z2, Canada.
ORCID: 0000-0002-1917-8330

Research Interests

• Probability and statistical mechanics, with special interest in models including spin systems, percolation, self-avoiding walk, branched polymers, and their (near-)critical phenomena.
• I work with the lace expansion, which is a method to analyse high-dimensional models.

Preprints and Publications

1. Y. Liu. High-dimensional long-range statistical mechanical models have random walk correlation functions. Feb 17, 2025.
   Preprint at arXiv.
2. Y. Liu, J. Park and G. Slade. Universal finite-size scaling in high-dimensional critical phenomena. Dec 11, 2024.
   Preprint at arXiv.
3. Y. Liu and G. Slade. Critical scaling profile for trees and connected subgraphs on the complete graph. Dec 7, 2024.
   Preprint at arXiv.
4. Y. Liu. Gaussian deconvolution on ℝ^d with application to self-repellent Brownian motion. Nov 25, 2024.
   Preprint at arXiv.
5. Y. Liu, R. Panis and G. Slade. The torus plateau for the high-dimensional Ising model. May 27, 2024.
   Preprint at arXiv.
6. Y. Liu. A general approach to massive upper bound for two-point function with application to self-avoiding walk torus plateau. Oct 26, 2023.
   Preprint at arXiv.
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 and G. Slade. Gaussian deconvolution and the lace expansion for spread-out models. To appear in Ann. Inst. H. Poincaré Probab. Statist.
   arXiv
9. Y. Liu and G. Slade. Gaussian deconvolution and the lace expansion. Probab. Theory Relat. Fields, (2024).
   arXiv
10. 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. The torus plateau for the high-dimensional Ising model.
   Feb 5, 2025 at UBC Probability seminar.
2. The torus plateau for the high-dimensional Ising model.
   Dec 1, 2024 at CMS Winter Meeting, Discrete Probability session.
3. Continuous-time weakly self-avoiding walk on ℤ has strictly monotone escape speed.
   July 9, 2024 at Self-interacting processes at University of Cambridge.
   Video
4. Gaussian deconvolution and the lace expansion.
   Dec 15, 2023 at Random Interacting Systems, Scaling Limits, and Universality at National University of Singapore.
   Slides
5. Gaussian deconvolution and the lace expansion.
   Nov 22, 2023 at UBC Probability seminar.
6. Continuous-time weakly self-avoiding walk on ℤ has strictly monotone escape speed.
   Oct 25, 2023 at SALSIS 2023 at Kyoto University.
7. Continuous-time weakly self-avoiding walk on ℤ has strictly monotone escape speed.
   Sept 21, 2022 at UBC Probability seminar.

Teaching