Replica Fourier Transforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices

The analysis of objects living on ultrametric trees, in particular the block-diagonalization of 4-replica matrices $M^{αβ; γδ}$, is shown to be dramatically simplified through the introduction of properly chosen operations on those objects. These are the Replica Fourier Transforms on ultrametric trees. Those transformations are defined and used in the present work.

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