Asymptotics of Symmetric Polynomials: A Dynamical Point of View
Alice Guionnet, Jiaoyang Huang · 2026
Read Asymptotics of Symmetric Polynomials: A Dynamical Point of View by Alice Guionnet, Jiaoyang Huang (2026) in the Tower of Babel, a free online library of public-domain works preserved in clean, searchable text. No sign-up. The full text is served as a plain-text file at a predictable URL, where text is present: https://antarctic-labs.com/tower-of-babel/pmc-13242455.txt.
Description
Alice Guionnet and Jiaoyang Huang studied two famous families of symmetric polynomials in the limit as their variable count grows without bound. Their paper appeared in Communications in Mathematical Physics in 2026. Macdonald and Jack polynomials sit at the crossroads of algebra, probability, and physics, but their large-scale behavior had resisted a full description. The authors characterize the limits through variational problems, where an energy-like quantity is minimized.
A key step proves a large deviation principle for a deformed version of non-intersecting random walks. At the special value of one, those walks match random lozenge tilings of strip-shaped domains. That connection lets the paper recover a celebrated tiling result of Cohn and co-authors by a new route. It then extends the principle to every positive value. The work ties polynomial limits to the study of random surfaces.
Catalog record
| CREATOR | Alice Guionnet, Jiaoyang Huang |
|---|---|
| YEAR | 2026 |
| COLLECTION | PAPERS |
| FORMAT | TXT |
| FILE SIZE | 129 KB |
| VERSION | 1.0 |
| LICENSE | CC BY 4.0 |
| RIGHTS | CC BY |
| SOURCE | Europe PMC |