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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A numerical investigation into the scaling behavior of the longest increasing subsequences of the symmetric ultra-fat tailed random walk

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Author(s):
Ricardo, J. [1] ; Mendonca, G. [1]
Total Authors: 2
Affiliation:
[1] Univ Sao Paulo, Escola Artes Ciencias & Humanidades, Rua Arlindo Bettio 1000, BR-03828000 Sao Paulo, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: Physics Letters A; v. 384, n. 29 OCT 19 2020.
Web of Science Citations: 0
Abstract

The longest increasing subsequence (LIS) of a sequence of correlated random variables is a basic quantity with potential applications that has started to receive proper attention only recently. Here we investigate the behavior of the length of the LIS of the so-called symmetric ultra-fat tailed random walk, introduced earlier in an abstract setting in the mathematical literature. After explicit constructing the ultra-fat tailed random walk, we found numerically that the expected length L-n of its LIS scales with the length n of the walk like < L-n > similar to n(0.716) indicating that, indeed, as far as the behavior of the LIS is concerned the ultra-fat tailed distribution can be thought of as equivalent to a very heavy tailed alpha-stable distribution. We also found that the distribution of L-n seems to be universal, in agreement with results obtained for other heavy tailed random walks. (C) 2020 Elsevier B.V. All rights reserved. (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
FAPESP's process: 20/04475-7 - Longest increasing subsequences of random walks and correlated time series
Grantee:José Ricardo Gonçalves de Mendonça
Support Opportunities: Regular Research Grants