Probabilistic estimates for tensor products of random vectors

TL;DR

This paper develops probabilistic bounds for tensor products of random vectors and applies these results to embed specific matrix spaces into the L1 space, advancing understanding of high-dimensional probabilistic embeddings.

Contribution

It introduces new probabilistic estimates for tensor products of random vectors and demonstrates their application in embedding matrix spaces into L1.

Findings

Probabilistic bounds for tensor products established

Embedding of matrix spaces into L1 achieved

Enhanced understanding of high-dimensional probabilistic embeddings

Abstract

We prove some probabilistic estimates for tensor products of random vectors. As an application we obtain embeddings of certain matrix spaces into $L_1$.