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

Journal of the European Mathematical Society (2008)

- Volume: 010, Issue: 4, page 987-1011
- ISSN: 1435-9855

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topBourgain, 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 -

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