https://github.com/chenle02/directed-polymers-shenzhen-2026
Slide deck: A class of d-dimensional directed polymers in a Gaussian environment (CUHK-Shenzhen, May 6 2026)
https://github.com/chenle02/directed-polymers-shenzhen-2026
directed-polymers mathematics mathjax presentation-slides reveal-js spde
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Slide deck: A class of d-dimensional directed polymers in a Gaussian environment (CUHK-Shenzhen, May 6 2026)
- Host: GitHub
- URL: https://github.com/chenle02/directed-polymers-shenzhen-2026
- Owner: chenle02
- Created: 2026-05-06T06:22:26.000Z (3 months ago)
- Default Branch: main
- Last Pushed: 2026-05-06T06:36:00.000Z (3 months ago)
- Last Synced: 2026-05-06T08:39:22.288Z (3 months ago)
- Topics: directed-polymers, mathematics, mathjax, presentation-slides, reveal-js, spde
- Language: HTML
- Homepage: https://chenle02.github.io/directed-polymers-shenzhen-2026/
- Size: 16.5 MB
- Stars: 0
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
README
# A Class of *d*-Dimensional Directed Polymers in a Gaussian Environment
### Workshop on PDEs and Stochastic PDEs in Material Science and Statistical Mechanics
**The Chinese University of Hong Kong, Shenzhen** · May 4–8, 2026
[](https://chenle02.github.io/directed-polymers-shenzhen-2026/)
[](https://revealjs.com)
[](https://www.mathjax.org/)
[](https://www.manim.community/)
[](https://arxiv.org/abs/2603.06574)
[](https://creativecommons.org/licenses/by/4.0/)
---
## ▶ View the Slides
**Live deployment:**
| Key | Action |
|-----|--------|
| `→` `Space` | Advance |
| `←` | Back |
| `Esc` / `O` | Overview (jump by clicking a tile) |
| `S` | Speaker view (clock, timer, next-slide preview) |
| `F` | Fullscreen |
| `?` (Shift+/) | Help dialog |
---
## 🎤 The Talk
A research-colloquium slide deck by **Le Chen** ([Auburn University](https://chenle02.github.io)), 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**
---
## 📄 Preprint
> L. Chen, C. Ouyang, S. Tindel, P. Xia,
> *A class of d-dimensional directed polymers in a Gaussian environment.*
> [**arXiv:2603.06574**](https://arxiv.org/abs/2603.06574) (2026).
---
## 📖 About the Talk
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.
### Central results
1. **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 $\beta > 0$.
2. **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.
3. **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.
### Manim animations
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
---
## 🏗️ Built With
- [**Reveal.js 5.0.5**](https://revealjs.com) — slide framework, `night` theme
- [**MathJax 3**](https://www.mathjax.org/) — TeX rendering (CDN)
- [**Manim Community**](https://www.manim.community/) — open-source mathematical animations
- [**edge-tts**](https://github.com/rany2/edge-tts) — narration
### Local preview
```bash
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
```
---
## 🗂️ Repository Layout
```
.
├── 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)
```
---
## 🙏 Acknowledgments
This work is supported by:
- **U.S. National Science Foundation** — CAREER Award
[No. 2443823](https://www.nsf.gov/awardsearch/showAward?AWD_ID=2443823) (2025–2030)
- **Simons Foundation** — Travel Support for Mathematicians
No. 959981 (2022–2027)
The mathematical animations were built with the
[**Manim Community**](https://www.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](https://creativecommons.org/licenses/by/4.0/).*
*Reveal.js, MathJax, Manim, and other third-party code retain their respective licenses.*
**谢谢 · Thank You**