Abstract
We prove that, at every positive temperature, the infinite-volume free energy of the one-dimensional log-gas, or beta-ensemble, has a unique minimizer, which is the Sine-beta process arising from random matrix theory. We rely on a quantitative displacement convexity argument at the level of point processes, and on the screening procedure introduced by Sandier-Serfaty.
| Original language | English |
|---|---|
| Pages (from-to) | 615-675 |
| Number of pages | 61 |
| Journal | Communications on Pure and Applied Mathematics |
| Volume | 74 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Mar 2021 |
| Externally published | Yes |