On the injective norm of random tensors

Stéphane DARTOIS
École Polytechnique

Date(s) : 10/02/2026 iCal
14h30 - 15h30

In this talk, I will present the results
of a collaboration with Benjamin McKenna
on the injective norm of large random tensors
and random quantum states,
and describe some of the underlying context.
The injective norm is a natural generalization to tensors
of the operator norm of a matrix
and appears in multiple fields.
In quantum information,
the injective norm is one important measure
of genuine multipartite entanglement of quantum states,
known as geometric entanglement.
I will discuss how we first used
an approach based on Kac-Rice formula
to obtain upper bounds on the injective norm
of random Gaussian tensors,
that we believe to be tight.
If time allows,
I will also discuss ongoing works,
in which we develop what we believe to be
a new, much simpler approach to this question,
allowing us to recover some of our Kac-Rice results
and extend them beyond the Gaussian case.