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Characteristic polynomials of random truncations: moments, duality and asymptotics
journal contribution
posted on 2023-06-10, 04:11 authored by Alexander Serebryakov, Nicholas SimmNicholas Simm, Guillaume DubachWe study moments of characteristic polynomials of truncated Haar distributed matrices from the three classical compact groups O(N), U(N) and Sp(2N). For finite matrix size we calculate the moments in terms of hypergeometric functions of matrix argument and give explicit integral representations highlighting the duality between the moment and the matrix size as well as the duality between the orthogonal and symplectic cases. Asymptotic expansions in strong and weak non-unitarity regimes are obtained. Using the connection to matrix hypergeometric functions, we establish limit theorems for the log-modulus of the characteristic polynomial evaluated on the unit circle.
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Publication status
- Published
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- Accepted version
Journal
Random Matrices: Theory and ApplicationISSN
2010-3271Publisher
World Scientific Publishing Co. Pte LtdExternal DOI
Page range
1-17Department affiliated with
- Mathematics Publications
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- No
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- Yes
Legacy Posted Date
2022-07-05First Compliant Deposit (FCD) Date
2022-07-05Usage metrics
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