Decomposing Tensor Spaces via Path Signatures
Representation Theory
2024-12-10 v2 Algebraic Geometry
Probability
Abstract
The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors at a particular level gives rise to the universal signature variety. We show that the parametrization of this variety induces a natural decomposition of the tensor space via representation theory, and connect this to the study of path invariants. We also reveal certain constraints that apply to the rank and symmetry of a signature tensor.
Keywords
Cite
@article{arxiv.2308.11571,
title = {Decomposing Tensor Spaces via Path Signatures},
author = {Carlos Améndola and Francesco Galuppi and Ángel David Ríos Ortiz and Pierpaola Santarsiero and Tim Seynnaeve},
journal= {arXiv preprint arXiv:2308.11571},
year = {2024}
}
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23 pages