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Creators/Authors contains: "Wasilewski, Mateusz"

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  1. ; ; ; ; (, Journal of the London Mathematical Society)
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  2. ; (, Transactions of the American Mathematical Society)
    We prove a number of results to the effect that generic quantum graphs (defined via operator systems as in the work of Duan-Severini-Winter / Weaver) have few symmetries: for a Zariski-dense open set of tuples ( X 1 , ⋯ , X d ) (X_1,\cdots ,X_d) of traceless self-adjoint operators in the n × n n\times n matrix algebra the corresponding operator system has trivial automorphism group, in the largest possible range for the parameters: 2 ≤ d ≤ n 2 − 3 2\le d\le n^2-3 . Moreover, the automorphism group is generically abelian in the larger parameter range 1 ≤ d ≤ n 2 − 2 1\le d\le n^2-2 . This then implies that for those respective parameters the corresponding random-quantum-graph model built on the GUE ensembles of X i X_i ’s (mimicking the Erdős-Rényi G ( n , p ) G(n,p) model) has trivial/abelian automorphism group almost surely. 
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  3. ; ; ; ; ; ; (, Communications in Mathematical Physics)
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  4. ; ; (, Journal of Functional Analysis)
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