115 citations · 286 across the 19 of their papers we have counts for
9 papers · 1 filter
Large factorization of families of tensor trace-invariants
Sylvain Carrozza, Johann Chevrier, Luca Lionni
It was recently proven that, in contrast to their matrix analogues, the moments of a real Gaussian tensor of size N do not in general factorize over their connected components in t…
Properties of tensorial free cumulants
Thomas Buc-d'Alché, Luca Lionni
In the past two years, several points of view have been proposed to address the question of the generalization of the theory of free probability to random tensors with different in…
Tensor invariants for multipartite entanglement classification
Sylvain Carrozza, Johann Chevrier, Luca Lionni
Organising the space of entanglement structures of a multipartite quantum system is a much more challenging task than its bipartite version: while the local unitary (LU) orbit of a…
Free cumulants and freeness for unitarily invariant random tensors
Benoit Collins, Razvan Gurau, Luca Lionni
We address the question of the asymptotic description of random tensors that are local-unitary invariant, that is, invariant by conjugation by tensor products of independent unitar…
The tensor Harish-Chandra--Itzykson--Zuber integral II: detecting entanglement in large quantum systems
Benoît Collins, Razvan Gurau, Luca Lionni
We consider the recently introduced generalization of the Harish-Chandra--Itzykson--Zuber integral to tensors and discuss its asymptotic behavior when the characteristic size N of…
One-matrix differential reformulation of two-matrix models
Joren Brunekreef, Luca Lionni, Johannes Thürigen
Differential reformulations of field theories are often used for explicit computations. We derive a one-matrix differential formulation of two-matrix models, with the help of which…
Melonic Turbulence
Stéphane Dartois, Oleg Evnin, Luca Lionni +2
We propose a new application of random tensor theory to studies of non-linear random flows in many variables. Our focus is on non-linear resonant systems which often emerge as weak…
Colored discrete spaces: higher dimensional combinatorial maps and quantum gravity
Luca Lionni
In any dimension , the Euclidean Einstein-Hilbert action, which describes gravity in the absence of matter, can be discretized over random discrete spaces obtained by gluing fam…
Note on the Intermediate Field Representation of Phi^2k Theory in Zero Dimension
Luca Lionni, Vincent Rivasseau
This expanded version corrects some misprints of the first version, details completely the poof of Borel-Leroy summability and for in the complex case provides a new improved…