Random Walks on
نویسنده
چکیده
We introduce two new techniques to the analysis on fractals. One is based on the presentation of the fractal as the boundary of a countable Gromov hyperbolic graph, whereas the other one consists in taking all possible \backward" extensions of the above hyperbolic graph and considering them as the classes of a discrete equivalence relation on an appropriate compact space. Illustrating these techniques on the example of the Sierpi nski gasket (the associated hyperbolic graph is called the Sierpi nski graph), we show that the Sierpi nski gasket can be identiied with the Martin and the Poisson boundaries for fairly general classes of Markov chains on the Sierpi nski graph.
منابع مشابه
A PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS
A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...
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