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Optimality of finite field dimension expanders
Urban Jezernik, Markus Reineke
Source abstract
We show that random tuples of matrices over a finite field are uniform dimension expanders for every expansion coefficient below the optimal one, using elementary counting arguments. The same holds for the optimal coefficient along a set of dimensions of density 1. By contrast, along Fibonacci dimensions random pairs of matrices fail to be optimal dimension expanders with probability bounded away from zero.
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