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

Author

Listed:
  • Charles S. do Amaral

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

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¯.

Suggested Citation

  • Charles S. do Amaral, 2024. "A note about the maximum local time of a random walk on the square lattice," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 35(02), pages 1-6, February.
    • Handle: RePEc:wsi:ijmpcx:v:35:y:2024:i:02:n:s0129183124500190
    DOI: 10.1142/S0129183124500190
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