Replica Fourier Transforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices
C. De Dominicis, D.M. Carlucci, T. Temesvari
TL;DR
This paper introduces Replica Fourier Transforms on ultrametric trees to simplify the block-diagonalization of multi-replica matrices, enhancing analytical techniques in ultrametric space analysis.
Contribution
The paper defines and applies Replica Fourier Transforms on ultrametric trees, providing a new method to simplify the analysis of multi-replica matrices.
Findings
Simplified block-diagonalization of 4-replica matrices.
Defined new operations called Replica Fourier Transforms.
Enhanced analytical tools for ultrametric structures.
Abstract
The analysis of objects living on ultrametric trees, in particular the block-diagonalization of 4-replica matrices , 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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