Logarithmic-Sobolev and Poincaré inequalities for the simple random walk on the Hanoi graph
We obtain a Poincaré and a logarithmitc sobolev inequality for the simple random walk on the Hanoi graph. These results imply upper bounds of order (3/2)^m on the relaxation time and on the inverse of the log-Sobolev constant of this process. In particular, we prove that the mixing time of this random walk is of order O ( (3/2)^{m} \log m ). Our method can be used for other random walks on fractal discretizations. |