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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Asymptotic behavior of the length of the longest increasing subsequences of random walks

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Autor(es):
Mendonca, J. Ricardo G. [1, 2] ; Schawe, Hendrik [3, 4] ; Hartmann, Alexander K. [3]
Número total de Autores: 3
Afiliação do(s) autor(es):
[1] Univ Sao Paulo, Escola Artes Ciencias & Humanidades, BR-03828000 Sao Paulo - Brazil
[2] Univ Paris Saclay, Univ Paris Sud, LPTMS, CNRS UMR 8626, F-91405 Orsay - France
[3] Carl von Ossietzky Univ Oldenburg, Inst Phys, D-26111 Oldenburg - Germany
[4] CY Cergy Paris Univ, Lab Phys Theor & Modelisat, CNRS UMR 8089, F-95000 Cergy - France
Número total de Afiliações: 4
Tipo de documento: Artigo Científico
Fonte: Physical Review E; v. 101, n. 3 MAR 4 2020.
Citações Web of Science: 0
Resumo

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)

Processo FAPESP: 17/22166-9 - Recordes, alcance e maiores subsequências crescentes de passeios aleatórios
Beneficiário:José Ricardo Gonçalves de Mendonça
Linha de fomento: Bolsas no Exterior - Pesquisa