Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Induced measures of simple random walks on Sierpinski graphs   In \cite{[K]}, Kaimanovich defined an augmented rooted tree $(X, E)$
corresponding to the Sierpinski gasket $K$, and showed that the Martin boundary
of the simple random walk $\{Z_n\}$ on it is homeomorphic to $K$. It is of
interest to determine the hitting distributions $v_{{\bf x}}(\cdot) =
{\mathbb{P}}_{{\bf x}}\{\lim_{n \rightarrow \infty} Z_n \in \cdot\}$ induced on
$K$. Using a reflection principle based on the symmetries of $K$, we show that
if the walk starts at the root of $(X, E)$, the hitting distribution is exactly
the normalized Hausdorff measure $\mu$ on $K$. In particular, each $v_{{\bf
x}}$, ${\bf x} \in X$, is absolutely continuous with respect to $\mu$. This
answers a question of Kaimanovich [K, Problem 4.14]. The argument can be
generalized to other symmetric self-similar sets.

8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg