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

Autor(es)

Ricardo, J. ^[1] ; Mendonca, G. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Escola Artes Ciencias & Humanidades, Rua Arlindo Bettio 1000, BR-03828000 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Physics Letters A; v. 384, n. 29 OCT 19 2020.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 17/22166-9 - Recordes, alcance e maiores subsequências crescentes de passeios aleatórios
• Beneficiário: José Ricardo Gonçalves de Mendonça
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 20/04475-7 - Maiores subsequências crescentes de passeios aleatórios e séries temporais correlacionadas
• Beneficiário: José Ricardo Gonçalves de Mendonça
• Modalidade de apoio: Auxílio à Pesquisa - Regular