Injective norm of random tensors with independent entries

TL;DR

This paper establishes a non-asymptotic bound for the expected injective norm of random tensors with independent entries, extending techniques from matrix spectral norm bounds to higher-order tensors.

Contribution

It introduces a novel non-asymptotic bound for the injective norm of random tensors, generalizing known matrix results to tensors with independent entries.

Findings

Provides a bound similar to Bandeira and van Handel's for matrices

Extends spectral norm bounds to tensor injective norms

Offers tools for analyzing random tensors in high-dimensional settings

Abstract

We obtain a non-asymptotic bound for the expected injective norm of a random tensor with independent entries. This bound is similar to the bound by Bandeira and van Handel (2016) for the expected spectral norm of a random matrix with independent entries.