@article{c6470f3031084cce8d18199a4cd6ace0,
title = "Lamplighter Random Walks on Fractals",
abstract = "We consider on-diagonal heat kernel estimates and the laws of the iterated logarithm for a switch-walk-switch random walk on a lamplighter graph under the condition that the random walk on the underlying graph enjoys sub-Gaussian heat kernel estimates.",
keywords = "Fractals, Heat kernels, Laws of the iterated logarithm (LILs), Random walks, Sub-Gaussian estimates, Wreath products",
author = "Takashi Kumagai and Chikara Nakamura",
note = "Funding Information: We would like to thank Martin T. Barlow for stimulating discussions when this project was initiated. We also thank the anonymous referee for detailed comments and careful corrections. Especially, we are grateful to the referee for pointing out to us that Theorem (II) and Lemma require only the on-diagonal heat kernel upper bound () rather than the full upper bound (). The first author was partially supported by JSPS KAKENHI Grant Number 25247007. The second author was partially supported by JSPS KAKENHI Grant Number 15J02838. Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media New York.",
year = "2018",
month = mar,
day = "1",
doi = "10.1007/s10959-016-0718-0",
language = "English",
volume = "31",
pages = "68--92",
journal = "Journal of Theoretical Probability",
issn = "0894-9840",
publisher = "Springer New York",
number = "1",
}