Maximum-Entropy Inference and Inverse Continuity of the Numerical Range

We study the continuity of the maximum-entropy inference map for two observables in finite dimensions. We prove that the continuity is equivalent to the strong continuity of the set-valued inverse numerical range map. This gives a continuity condition in terms of analytic eigenvalue functions which...

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Bibliographic Details
Published in:Reports on mathematical physics 2016-04, Vol.77 (2), p.251-263
Main Author: Weis, Stephan
Format: Article
Language:English
Subjects:
47A12
54C10
62F30
82B26
94A17
continuity
Continuity (mathematics)
Discontinuity
Eigenvalues
Equivalence
Inference
Inverse
Mathematical analysis
Mathematical models
maximum-entropy inference
numerical range
Primary 81P16
Secondary 47N50
stability
strong continuity
strong stability
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Summary:We study the continuity of the maximum-entropy inference map for two observables in finite dimensions. We prove that the continuity is equivalent to the strong continuity of the set-valued inverse numerical range map. This gives a continuity condition in terms of analytic eigenvalue functions which implies that discontinuities are very rare. It shows also that the continuity of the MaxEnt inference method is independent of the prior state.
ISSN:0034-4877
1879-0674
DOI:10.1016/S0034-4877(16)30022-2