The Chinese University of Hong Kong, Shenzhen · May 4–8, 2026
Live deployment: https://chenle02.github.io/directed-polymers-shenzhen-2026/
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A research-colloquium slide deck by Le Chen (Auburn University), joint work with
| Co-author | Affiliation |
|---|---|
| Cheng Ouyang | University of Illinois at Chicago |
| Samy Tindel | Purdue University |
| Panqiu Xia | Cardiff University |
Wednesday, May 6, 2026 · 16:00–17:00 · CUHK-Shenzhen, Conference Complex II 202 & 203
L. Chen, C. Ouyang, S. Tindel, P. Xia, A class of d-dimensional directed polymers in a Gaussian environment. arXiv:2603.06574 (2026).
The talk introduces a class of d-dimensional continuous directed polymers in a general Gaussian environment — white in time, homogeneous in space — covering both trace-class and non-trace-class regimes.
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Singularity dichotomy. The quenched polymer measure
$\mathbb{P}^W_\beta$ is mutually singular with the Wiener measure$\mathbb{P}_0$ for almost every realization of the noise$W$ if and only if the spatial covariance is not trace-class, i.e.$\widehat{f}(\mathbb{R}^d) = \infty$ . The criterion is sharp and holds for every$\beta > 0$ . -
Diffusive CLT in
$d \ge 3$ at high temperature. Under Dalang's spectral integrability$\Upsilon(0) < \infty$ and weak disorder$\beta < \beta_0$ , the rescaled polymer endpoint converges to a Gaussian limit. -
Local Brownian behavior. Despite the global singularity, the polymer path agrees with a Brownian motion at every fixed scale — singularity emerges only in the limit.
Three Manim-rendered scenes carry the main ideas:
- Scene A — Discrete → continuous polymer via Donsker refinement
- Scene B — Brownian motion vs. polymer path (locally identical, globally singular)
- Scene C — Martingale collapse on a dyadic skeleton
- Reveal.js 5.0.5 — slide framework,
nighttheme - MathJax 3 — TeX rendering (CDN)
- Manim Community — open-source mathematical animations
- edge-tts — narration
git clone https://github.com/chenle02/directed-polymers-shenzhen-2026.git
cd directed-polymers-shenzhen-2026
python3 -m http.server 8000
# Open http://localhost:8000 in your browser.
├── index.html ← The slide deck
├── mystyle_polymer.css ← Custom styling (overrides night theme)
├── dist/ ← Reveal.js core
├── plugin/ ← Reveal.js plugins (notes, math, highlight)
├── assets/ ← Images (Jupiter, team, Bessel, SPDE landscapes)
└── videos/ ← Manim animations (scene_A–D.mp4)
This work is supported by:
- U.S. National Science Foundation — CAREER Award No. 2443823 (2025–2030)
- Simons Foundation — Travel Support for Mathematicians No. 959981 (2022–2027)
The mathematical animations were built with the Manim Community open-source library — warm thanks to the community of contributors who maintain it.
I am grateful to the Workshop on PDEs and SPDEs in Material Science and Statistical Mechanics organizers at CUHK-Shenzhen — Yuan Chen, Cheuk Yin Lee, and Xuefeng Wang — for the kind invitation, and to Bella Lin (SSE) for impeccable logistics support.
Special thanks to my coauthors Cheng Ouyang, Samy Tindel, and Panqiu Xia for the long collaboration that produced this work, and to the broader SPDE community whose ideas this talk builds upon.
Slides © 2026 Le Chen — released under CC BY 4.0. Reveal.js, MathJax, Manim, and other third-party code retain their respective licenses.
谢谢 · Thank You