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We prove using a novel random matrix model that all right-angled Artin groups have a sequence of finite dimensional unitary representations that strongly converge to the regular representation.
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Wojciech Młotkowski, Λ \Lambda -free probability , Infin. Dimens. Anal. Quantum Probab. Relat. Top. 7
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U. Haagerup and S. Thorbjørnsen, A new application of random matrices: Ext ( C red ∗ ( F 2 ) ) \mathrm{Ext}(C^{*}_{\mathrm{red}}(F_{2})) is not a group , Ann. of Math. (2) 162
2005
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Nathanial P. Brown and Narutaka Ozawa, C ∗ C^{*} -algebras and finite-dimensional approximations , Grad. Stud. Math., vol. 88, Providence, RI: American Mathematical Society (AMS), 2008 (English)
2008
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Frédéric Haglund and Daniel T. Wise, Special cube complexes , Geom. Funct. Anal. 17
2008
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Nicolas Bergeron, Frédéric Haglund, and Daniel T. Wise, Hyperplane sections in arithmetic hyperbolic manifolds , J. Lond. Math. Soc., II. Ser. 83
2011
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D. Puder, Expansion of random graphs: new proofs, new results , Invent. Math. 201
2015
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Roland Speicher and Janusz Wysoczański, Mixtures of classical and free independence , Arch. Math. 107
2016
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Aaron Tikuisis, Stuart White, and Wilhelm Winter, Quasidiagonality of nuclear C ∗ C^{*} -algebras , Ann. Math. (2) 185
2017
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Chris Hall, Doron Puder, and William F. Sawin, Ramanujan coverings of graphs , Adv. Math. 323
2018
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Charles Bordenave and Benoît Collins, Eigenvalues of random lifts and polynomials of random permutation matrices , Ann. of Math. (2) 190
2019
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2012
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2012
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Camille Male, The norm of polynomials in large random and deterministic matrices, with appendix by D. Shlyakhtenko , Probab. Theory Relat. Fields 154
2012
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Daniel T. Wise, From riches to Raags: 3-manifolds, right-angled Artin groups, and cubical geometry. , CBMS Reg. Conf. Ser. Math., vol. 117, Providence, RI: American Mathematical Society (AMS); Washington, DC: Conference Board of the Mathematical Sciences (CBMS), 2012 (English)
2012
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Ian Agol, The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning). , Doc. Math. 18
2013
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Benoît Collins and Camille Male, The strong asymptotic freeness of Haar and deterministic matrices , Ann. Sci. Éc. Norm. Supér. (4) 47
2014
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2014
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2019
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2021
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2022
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Benoît Collins, Alice Guionnet, and Félix Parraud, On the operator norm of non-commutative polynomials in deterministic matrices and iid GUE matrices , Camb. J. Math. 10
2022
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Will Hide and Michael Magee, Near optimal spectral gaps for hyperbolic surfaces , Ann. Math. (2) 198
2023
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