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arXiv · 1705.11014

Congruent families and invariant tensors

Lorenz Schwachhöfer·Nihat Ay·Jürgen Jost·Hông Vân Lê
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Abstract

Classical results of Chentsov and Campbell state that -- up to constant multiples -- the only $2$-tensor field of a statistical model which is invariant under congruent Markov morphisms is the Fisher metric and the only invariant $3$-tensor field is the Amari-Chentsov tensor. We generalize this result for arbitrary degree $n$, showing that any family of $n$-tensors which is invariant under congruent Markov morphisms is algebraically generated by the canonical tensor fields defined in an earlier paper.

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Lorenz Schwachhöfer, Nihat Ay, Jürgen Jost, Hông Vân Lê. 2017-05-31. Congruent families and invariant tensors. https://arxiv.org/abs/1705.11014

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