Scale Invariance of the PNG Droplet and the Airy Process
| dc.creator | Praehofer, Michael | |
| dc.creator | Spohn, Herbert | |
| dc.date | 2001-05-29 | |
| dc.date | 2002-04-24 | |
| dc.date.accessioned | 2026-07-07T04:41:54Z | |
| dc.date.available | 2026-07-07T04:41:54Z | |
| dc.description | We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process A(y). The Airy process is stationary, it has continuous sample paths, its single "time" (fixed y) distribution is the Tracy-Widom distribution of the largest eigenvalue of a GUE random matrix, and the Airy process has a slow decay of correlations as y^(-2). Roughly the Airy process describes the last line of Dyson's Brownian motion model for random matrices. Our construction uses a multi-layer version of the PNG model, which can be analyzed through fermionic techniques. Specializing our result to a fixed value of y, one reobtains the celebrated result of Baik, Deift, and Johansson on the length of the longest increasing subsequence of a random permutation. | |
| dc.description | 32 pages, 1 eps, revised version, the multi-layer dynamics now has two variants, simpler proof of Thm 2.1 | |
| dc.identifier | https://arxiv.org/abs/math/0105240 | |
| dc.identifier | http://arxiv.org/abs/math/0105240 | |
| dc.identifier | J. Stat. Phys. 108 (5-6): 1071-1106 (2002) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61553 | |
| dc.subject | Probability | |
| dc.subject | Statistical Mechanics | |
| dc.title | Scale Invariance of the PNG Droplet and the Airy Process | |
| dc.type | text |