Transition density of diffusion on Sierpinski gasket and extension of Flory's formula

TL;DR

This paper investigates the transition density of diffusion on the Sierpinski gasket, extending Flory's formula for self-avoiding walks on fractals and providing evidence of oscillatory behavior in the transition density.

Contribution

It extends Flory's formula to fractal spaces and demonstrates oscillatory behavior of the transition density on the Sierpinski gasket.

Findings

Extended Flory's formula for fractals

Evidence of oscillatory transition density behavior

Numerical calculations supporting theoretical results

Abstract

Some problems related to the transition density u(t,x) of the diffusion on the Sierpinski gasket are considerd, based on recent rigorous results and detailed numerical calculations. The main contents are an extension of Flory's formula for the end-to-end distance exponent of self-avoiding walks on the fractal spaces, and an evidence of the oscillatory behavior of u(t,x) on the Sierpinski gasket.