![]() |
CiteULike |
![]() |
ansobol's CiteULike |
![]() |
![]() |
|
![]() |
Register | ![]() |
Log in | ![]() |
Scale Invariance of the PNG Droplet and the Airy Process Export |
Reviews
[Write a review of this article]
There are no reviews of this article
Find related articles from these CiteULike users
Find related articles with these CiteULike tags
Posting History
AbstractWe 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.
BibTeX record
RIS record| 295 | |
| 292 | |
| 241 | |
| 221 | |
| 213 | |
| 207 | |
| 195 | |
| 193 | |
| 185 | |
| 171 | |
| 166 | |
| 166 | |
| 159 | |
| 149 | |
| 128 | |
| 127 | |
| 127 | |
| 114 | |
| 108 | |
| 107 | |
| 106 | |
| 101 | |
| 99 | |
| 97 | |
| 94 | |
| 93 | |
| 92 | |
| 91 | |
| 88 | |
| 86 | |
| 85 | |
| 81 | |
| 75 | |
| 68 | |
| 65 | |
| 63 | |
| 61 | |
| 61 | |
| 58 | |
| 56 | |
| 55 | |
| 54 | |
| 53 | |
| 52 | |
| 51 | |
| 50 | |
| 50 | |
| 48 | |
| 48 | |
| 48 | |
| 47 | |
| 47 | |
| 47 | |
| 45 | |
| 44 | |
| 44 | |
| 44 | |
| 43 | |
| 43 | |
| 43 | |
| 42 | |
| 42 | |
| 41 | |
| 40 | |
| 38 | |
| 38 | |
| 36 | |
| 36 | |
| 36 | |
| 36 | |
| 35 | |
| 35 | |
| 35 | |
| 34 | |
| 34 | |
| 34 | |
| 33 | |
| 33 | |
| 33 | |
| 33 | |
| 32 | |
| 32 | |
| 31 | |
| 30 | |
| 30 | |
| 30 | |
| 29 | |
| 29 | |
| 28 | |
| 28 | |
| 27 | |
| 27 | |
| 27 | |
| 27 | |
| 27 | |
| 27 | |
| 26 | |
| 26 | |
| 26 | |
| 26 | |
| 26 | |
| 26 | |
| 25 | |
| 25 | |
| 25 | |
| 25 | |
| 24 | |
| 24 | |
| 24 | |
| 23 | |
| 23 | |
| 23 | |
| 23 | |
| 23 | |
| 22 | |
| 22 | |
| 22 | |
| 22 | |
| 22 | |
| 21 | |
| 21 | |
| 21 | |
| 20 | |
| 20 | |
| 20 | |
| 20 | |
| 20 | |
| 20 | |
| 20 | |
| 19 | |
| 19 | |
| 19 | |
| 19 | |
| 19 | |
| 19 | |
| 19 | |
| 19 | |
| 18 | |
| 18 | |
| 18 | |
| 18 | |
| 18 | |
| 18 | |
| 18 | |
| 18 | |
| 18 | |
| 18 | |
| 17 | |
| 17 | |
| 17 | |
| 17 | |
| 17 | |
| 17 | |
| 17 | |
| 17 | |
| 17 | |
| 17 | |
| 17 | |
| 17 | |
| 17 | |
| 17 | |
| 17 | |
| 16 | |
| 16 | |
| 16 | |
| 16 | |
| 16 | |
| 16 | |
| 16 | |
| 16 | |
| 16 | |
| 16 | |
| 16 | |
| 15 | |
| 15 | |
| 15 | |
| 15 | |
| 15 | |
| 15 | |
| 15 | |
| 15 | |
| 14 | |
| 14 | |
| 14 | |
| 14 | |
| 14 | |
| 14 | |
| 14 | |
| 14 | |
| 14 | |
| 14 | |
| 14 | |
| 14 | |
| 14 | |
| 14 | |
| 14 | |
| 14 | |
| 13 | |
| 13 | |
| 13 | |
| 13 | |
| 13 | |
| 13 | |
| 13 | |
| 13 | |
| 13 | |
| 13 | |
| 13 | |
| 13 | |
| 13 | |
| 13 | |
| 12 | |
| 12 | |
| 12 | |
| 12 | |
| 12 | |
| 12 | |
| 12 | |
| 12 | |
| 12 | |
| 12 | |
| 12 | |
| 12 | |
| 12 | |
| 12 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 11 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 10 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 9 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 8 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 7 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 6 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 5 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 4 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 3 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 2 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 | |
| 1 |


