A note about the maximum local time of a random walk on the square lattice

Charles S. do Amaral ()
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Charles S. do Amaral: Departamento de Matemática — Centro Federal de Educação, Tecnológica de Minas Gerais, Av. Amazonas 7675, Belo Horizonte, Minas Gerais, Brazil

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 02, 1-6

Abstract: This paper conducts a numerical analysis of the behavior of the average value of the Maximum Local Time, Ln∗, in the Simple Random Walk on the square lattice. It has been established in the literature that the sequence ζn:=(logn)2Ln∗ converges to π. The author found numerical evidence that the average value of ζn (ζn¯) increases until a certain value of n, denoted as nc, after which it decreases and approaches π. Furthermore, estimates are presented for nc and ζnc¯.

Keywords: Random walk; simple random walk; local time; maximum local time (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124500190

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