Scale Invariance of the PNG Droplet and the Airy Process Export

@article{citeulike:4972195, abstract = {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.}, archivePrefix = {arXiv}, author = {Praehofer, Michael and Spohn, Herbert}, citeulike-article-id = {4972195}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0105240}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0105240}, eprint = {math/0105240}, keywords = {airy-process}, month = {Apr}, posted-at = {2009-06-26 13:09:15}, priority = {2}, title = {Scale Invariance of the PNG Droplet and the Airy Process}, url = {http://arxiv.org/abs/math/0105240}, year = {2002} }

TY - JOUR ID - citeulike:4972195 L3 - citeulike-article-id:4972195 N2 - 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. TI - Scale Invariance of the PNG Droplet and the Airy Process KW - airy-process AU - Praehofer, Michael AU - Spohn, Herbert PY - 2002/Apr/24/ UR - http://arxiv.org/abs/math/0105240 ER -