Multifractals of Normalized First Passage Time in Sierpinski Gasket

TL;DR

This paper explores the multifractal properties of normalized first passage times on the Sierpinski gasket, using numerical methods to compare with lattice results, revealing complex scaling behaviors.

Contribution

It introduces a numerical analysis of the multifractal spectrum of first passage times on fractal structures, extending understanding beyond regular lattices.

Findings

Multifractal spectrum of first passage times is characterized on the Sierpinski gasket.

Normalized first passage times exhibit multifractal behavior similar to lattice systems.

Monte Carlo simulations effectively estimate generalized dimensions and spectra.

Abstract

The multifractal behavior of the normalized first passage time is investigated on the two dimensional Sierpinski gasket with both absorbing and reflecting barriers. The normalized first passage time for Sinai model and the logistic model to arrive at the absorbing barrier after starting from an arbitrary site, especially obtained by the calculation via the Monte Carlo simulation, is discussed numerically. The generalized dimension and the spectrum are also estimated from the distribution of the normalized first passage time, and compared with the results on the finitely square lattice.