| Full text | |
| Author(s): |
Mendonca, J. Ricardo G.
;
Schawe, Hendrik
;
Hartmann, Alexander K.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | PHYSICAL REVIEW E; v. 101, n. 3, p. 8-pg., 2020-03-04. |
| Abstract | |
We numerically estimate the leading asymptotic behavior of the length L-n of the longest increasing subsequence of random walks with step increments following Student's t -distribution with parameters in the range 1/2 <= nu <= 5. We find that the expected value E(L-n) similar to n(theta) In n, with theta decreasing from theta(nu = 1/2) approximate to 0.70 to theta(nu >= 5/2) approximate to 0.50. For random walks with a distribution of step increments of finite variance (nu > 2), this confirms previous observation of E(L-n) similar to root n In n to leading order. We note that this asymptotic behavior (including the subleading term) resembles that of the largest part of random integer partitions under the uniform measure and that, curiously, both random variables seem to follow Gumbel statistics. We also provide more refined estimates for the asymptotic behavior of E(L-n) for random walks with step increments of finite variance. (AU) | |
| FAPESP's process: | 17/22166-9 - Records, range, and longest increasing subsequences of random walks |
| Grantee: | José Ricardo Gonçalves de Mendonça |
| Support Opportunities: | Scholarships abroad - Research |