Expansion and random walks in ${\mathrm{SL}}_d(\mathbb{Z}/p^n\mathbb{Z})$: I

Bourgain, Jean, and Gamburd, Alex. "Expansion and random walks in $\mathrm {SL}_d(\mathbb {Z}/p^n\mathbb {Z})$: I." Journal of the European Mathematical Society 010.4 (2008): 987-1011. <http://eudml.org/doc/277735>.

@article{Bourgain2008,
abstract = {We prove that the Cayley graphs of $\mathrm \{SL\}_d(\mathbb \{Z\}/p^n\mathbb \{Z\})$ are expanders with respect to the projection of any fixed elements in $\mathrm \{SL\}_d(\mathbb \{Z\})$ generating a Zariski dense subgroup.},
author = {Bourgain, Jean, Gamburd, Alex},
journal = {Journal of the European Mathematical Society},
keywords = {Zariski dense subgroups; Cayley graphs; expander families},
language = {eng},
number = {4},
pages = {987-1011},
publisher = {European Mathematical Society Publishing House},
title = {Expansion and random walks in $\mathrm \{SL\}_d(\mathbb \{Z\}/p^n\mathbb \{Z\})$: I},
url = {http://eudml.org/doc/277735},
volume = {010},
year = {2008},
}

TY - JOUR
AU - Bourgain, Jean
AU - Gamburd, Alex
TI - Expansion and random walks in $\mathrm {SL}_d(\mathbb {Z}/p^n\mathbb {Z})$: I
JO - Journal of the European Mathematical Society
PY - 2008
PB - European Mathematical Society Publishing House
VL - 010
IS - 4
SP - 987
EP - 1011
AB - We prove that the Cayley graphs of $\mathrm {SL}_d(\mathbb {Z}/p^n\mathbb {Z})$ are expanders with respect to the projection of any fixed elements in $\mathrm {SL}_d(\mathbb {Z})$ generating a Zariski dense subgroup.
LA - eng
KW - Zariski dense subgroups; Cayley graphs; expander families
UR - http://eudml.org/doc/277735
ER -