QUANTUM WALKS ON SIERPINSKI GASKETS

Sierpinski Gaskets for Logic Functions Representation

This paper introduces a new approach to represent logic functions in the form of Sierpinski Gaskets. The structure of the gasket allows to manipulate with the corresponding logic expression using recursive essence of fractals. Thus, the Sierpinski gasket’s pattern has myriad useful properties which can enhance practical features of other graphic representations like decision diagrams. We have c...

Random Walks on Graphical Sierpinski Carpets

We consider random walks on a class of graphs derived from Sierpinski carpets. We obtain upper and lower bounds (which are non-Gaussian) on the transition probabilities which are, up to constants, the best possible. We also extend some classical Sobolev and Poincar e inequalities to this setting.

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...

Self-interacting self-avoiding walks on the Sierpinski gasket

Asymptotically One-dimensional Diiusions on the Sierpinski Gasket and the Abc-gaskets

Diiusion processes on the Sierpinski gasket and the abc-gaskets are constructed as limits of random walks. In terms of the associated renor-malization group, the present method uses the inverse trajectories which converge to unstable xed points corresponding to the random walks on one-dimensional chains. In particular, non-degenerate xed points are unnecessary for the construction. A limit theo...