Some properties of energy measures on Sierpinski gasket type fractals

Conformal Energy, Conformal Laplacian, and Energy Measures on the Sierpinski Gasket

On the Sierpinski Gasket (SG) and related fractals, we define a notion of conformal energy Eφ and conformal Laplacian ∆φ for a given conformal factor φ, based on the corresponding notions in Riemannian geometry in dimension n 6= 2. We derive a differential equation that describes the dependence of the effective resistances of Eφ on φ. We show that the spectrum of∆φ (Dirichlet or Neumann) has si...

Sampling on the Sierpinski Gasket

Random walks on the Sierpinski Gasket

The generating functions for random walks on the Sierpinski gasket are computed. For closed walks, we investigate the dependence of these functions on location and the bare hopping parameter. They are continuous on the infinite gasket but not differentiable. J. Physique 47 (1986) 1663-1669 OCTOBRE 1986, Classification Physics Abstracts 05.40 05.50 1. Preliminaries and review of known results. C...

Spanning Forests on the Sierpinski Gasket

We present the numbers of spanning forests on the Sierpinski gasket SGd(n) at stage n with dimension d equal to two, three and four, and determine the asymptotic behaviors. The corresponding results on the generalized Sierpinski gasket SGd,b(n) with d = 2 and b = 3, 4 are obtained. We also derive the upper bounds of the asymptotic growth constants for both SGd and SG2,b.

Interacting dimers on a Sierpinski gasket

The different manners of embedding subgraphs of many disjoint edges in a parent graph arise in several different chemical and physical contexts. The problem of enumeration, or more generally of weighted summation, of such embeddings seems quite difficult to treat quantitatively, at least for general extended graphs. The special extended parent graph treated here with the inclusion of interactio...