We prove a law of iterated logarithm for random walks on a family of diagonal products constructed by Brieussel and Zheng (2021). This provides a wide variety of new examples of law of iterated logarithm behaviors for random walks on groups. In particular, it follows that for any 21≤β≤1 there is a group G and random walk Wn on G with E∣Wn∣≃nβ such that
Classification :
05C81, 20E22, 20F69, 60B15, 60F15
Mots-clés :
random walks on groups, law of iterated logarithm, diagonal products, excursions
Affiliations des auteurs :
Gideon Amir
1
;
Guy Blachar
1
1
Bar-Ilan University, Ramat Gan, Israel
Gideon Amir; Guy Blachar. A law of iterated logarithm on lamplighter diagonal products. Groups, geometry, and dynamics, Tome 19 (2025) no. 3, pp. 1041-1080. doi: 10.4171/ggd/830
@article{10_4171_ggd_830,
author = {Gideon Amir and Guy Blachar},
title = {A law of iterated logarithm on lamplighter diagonal~products},
journal = {Groups, geometry, and dynamics},
pages = {1041--1080},
year = {2025},
volume = {19},
number = {3},
doi = {10.4171/ggd/830},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/830/}
}
TY - JOUR
AU - Gideon Amir
AU - Guy Blachar
TI - A law of iterated logarithm on lamplighter diagonal products
JO - Groups, geometry, and dynamics
PY - 2025
SP - 1041
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IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/830/
DO - 10.4171/ggd/830
ID - 10_4171_ggd_830
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%J Groups, geometry, and dynamics
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%R 10.4171/ggd/830
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