A Spectral Gap Theorem in $SU(d)$

By Jean Bourgain, Alex Gamburd. 2011

124 citations recorded by the source corpus.

We establish the spectral gap property for dense subgroups of $SU(d)$ ($d\geq 2$), generated by finitely many elements with algebraic entries; this result was announced in [BG3]. The method of proof differs, in several crucial aspects, from that used in [BG] in the case of SU(2).

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aadca69ff75deb52f49e9fe9820ba18c4ad8ea0a

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In Discrete Mathematics and Combinatorics

1. P. P. Varj'u
2. Adrian Ioana

In Geometry and Topology

1. P. P. Varj'u
2. Adrian Ioana

In Mathematical Physics

1. Michal Horodecki
2. P. P. Varj'u

Citations in the corpus

• Random walks in compact groups (2012, background): “We say that a profinite group G is (c, α)-quasirandom if for every irreducible unitary representation π of G, we have dimπ ≥ c[G : Ker(π)]α.”
• A spectral gap theorem in simple Lie groups (2014, unknown): “Note that this is exactly the case studied by Bourgain and Gamburd in [5].”
• Local random quantum circuits are approximate polynomial-designs: numerical results (2012, methodology): “[13] one can indeed do so, at least for a large class of gate sets: Corollary 7.”