Let be a set of elements of generating a Zariski dense subgroup of and let p be a sufficiently large prime. Consider the family of Cayley graphs , where we vary n. Then forms an expander family.
Soit un sous-ensemble de engendrant un sous-groupe de Zariski dense. On considère les graphes de Cayley , òu l'on varie n. Alors forment une famille d'expanseurs.
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Jean Bourgain 1; Alex Gamburd 1
@article{CRMATH_2008__346_11-12_619_0, author = {Jean Bourgain and Alex Gamburd}, title = {Random walks and expansion in $ {\mathrm{SL}}_{d}(\mathbb{Z}/{p}^{n}\mathbb{Z})$}, journal = {Comptes Rendus. Math\'ematique}, pages = {619--623}, publisher = {Elsevier}, volume = {346}, number = {11-12}, year = {2008}, doi = {10.1016/j.crma.2008.04.006}, language = {en}, }
TY - JOUR AU - Jean Bourgain AU - Alex Gamburd TI - Random walks and expansion in $ {\mathrm{SL}}_{d}(\mathbb{Z}/{p}^{n}\mathbb{Z})$ JO - Comptes Rendus. Mathématique PY - 2008 SP - 619 EP - 623 VL - 346 IS - 11-12 PB - Elsevier DO - 10.1016/j.crma.2008.04.006 LA - en ID - CRMATH_2008__346_11-12_619_0 ER -
Jean Bourgain; Alex Gamburd. Random walks and expansion in $ {\mathrm{SL}}_{d}(\mathbb{Z}/{p}^{n}\mathbb{Z})$. Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 619-623. doi : 10.1016/j.crma.2008.04.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.04.006/
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