Asymptotic behavior of the length of the longest increasing subsequences of random walks.
Phys Rev E
; 101(3-1): 032102, 2020 Mar.
Article
em En
| MEDLINE
| ID: mdl-32289985
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≤ν≤5. We find that the expected value E(L_{n})â¼n^{θ}lnn, with θ decreasing from θ(ν=1/2)≈0.70 to θ(ν≥5/2)≈0.50. For random walks with a distribution of step increments of finite variance (ν>2), this confirms previous observation of E(L_{n})â¼sqrt[n]lnn 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.
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1
Coleções:
01-internacional
Base de dados:
MEDLINE
Tipo de estudo:
Clinical_trials
Idioma:
En
Revista:
Phys Rev E
Ano de publicação:
2020
Tipo de documento:
Article
País de afiliação:
Brasil