Random Tensor

Random tensor analysis focuses on understanding the statistical properties and computational challenges of high-dimensional tensors with random entries, aiming to develop efficient algorithms for their decomposition and analysis. Current research emphasizes developing and analyzing spectral algorithms and power iteration methods for tensor decomposition, particularly in the overcomplete regime where the rank exceeds the dimension, often leveraging techniques from random matrix theory and tensor network representations. These advancements have implications for various fields, including machine learning (e.g., improving tensor factorization methods) and signal processing (e.g., enhancing noise-robust signal extraction from tensor data).