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Approximate Representations and Approximate Homomorphisms
[article]
2010
arXiv
pre-print
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_x,y ||f(xy) - f(x)f(y)||^2 is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities in
arXiv:1009.6230v1
fatcat:6p46odfe45bshe4lgp6uzxfepm