arXiv subjects

Kazuki Okamura

Publications and source records attributed to Kazuki Okamura.

38 records · Page 3Linked to original sources

arXiv2013

On the range of random walk on graphs satisfying a uniform condition

We consider the range of random walks up to time n, R_n, on graphs satisfying a uniform condition. This condition is characterized by potential theory. Not only all vertex transitive graphs but also many non-regular graphs satisfy the condition. We show certain weak laws of R_n from above and below. We also show that there is a graph such that it satisfies the condition and a sequence of the mean of R_n/n fluctuates. By noting the construction of the graph, we see that under the condition, the weak laws are best in a sense.

math.PR↗

arXiv2013

Singularity results for functional equations driven by linear fractional transformations

We consider functional equations driven by linear fractional transformations, which are special cases of de Rham's functional equations. We consider Hausdorff dimension of the measure whose distribution function is the solution. We give a necessary and sufficient condition for singularity. We also show that they have a relationship with stationary measures.

math.PR↗