Asymptotically One-dimensional Diiusions on the Sierpinski Gasket and the Abc-gaskets
نویسندگان
چکیده
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 theorem related to the discrete-time multi-type non-stationary branching processes is applied.
منابع مشابه
Asymptotically One-dimensional Diiusions on Scale-irregular Gaskets
A simple class of fractals which lack exact self-similarity is introduced, and the asymptotically one-dimensional diiusion process is constructed. The process moves mostly horizontally for very small scales, while for large scales it diiuses almost isotropically, in the sense of the oo-horizontal relative jump rate for the decimated random walks of the process. An essential step in the construc...
متن کاملAsymptotically one-dimensional diffusion on the Sierpinski gasket and multi-type branching processes with varying environment
Asymptotically one-dimensional diffusions on the Sierpinski gasket constitute a one parameter family of processes with significantly different behaviour to the Brownian motion. Due to homogenization effects they behave globally like the Brownian motion, yet locally they have a preferred direction of motion. We calculate the spectral dimension for these processes and obtain short time heat kerne...
متن کاملSierpinski 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...
متن کاملLee-Yang zeros and the Ising model on the Sierpinski Gasket
We study the distribution of the complex temperature zeros for the partition function of the Ising model on a Sierpinski gasket using an exact recursive relation. Although the zeros arrange on a curve pinching the real axis at T = 0 in the thermodynamic limit, their density vanishes asymptotically along the curve approaching the origin. This phenomenon explains the coincidence of the low temper...
متن کاملFractal behind smart shopping
The ‘minimal’ payment—a payment method which minimizes the number of coins in a purse—is presented. We focus on a time series of change given back to a shopper repeating the minimal payment. The delay plot shows visually that the set of successive change possesses a fine structure similar to the Sierpinski gasket. We also estimate effectivity of the minimal-payment method by means of the averag...
متن کامل