Decomposing Tensor Spaces via Path Signatures

Autor:	Améndola, Carlos, Galuppi, Francesco, Ortiz, Ángel David Ríos, Santarsiero, Pierpaola, Seynnaeve, Tim
Rok vydání:	2023
Předmět:	Mathematics - Representation Theory Mathematics - Algebraic Geometry Mathematics - Probability 60L10 60L70 05E10 15A72 14N07
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jpaa.2024.107807
Popis:	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 examine the question of determining what is the tensor rank of a signature tensor. Comment: 22 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2308.11571 Zobrazit plný text záznamu View this record from Arxiv