115 citations · 286 across the 19 of their papers we have counts for
21 papers
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…
From higher order free cumulants to non-separable hypermaps
Luca Lionni
Higher order free moments and cumulants, introduced by Collins, Mingo, Śniady and Speicher in 2006, describe the fluctuations of unitarily invariant random matrices in the limit of…
A family of triangulated 3-spheres constructed from trees
Timothy Budd, Luca Lionni
The search for universality in random triangulations of manifolds, like those featuring in (Euclidean) Dynamical Triangulations, is central to the random geometry approach to quant…
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…
The tensor Harish-Chandra-Itzykson-Zuber integral I: Weingarten calculus and a generalization of monotone Hurwitz numbers
Benoît Collins, Razvan Gurau, Luca Lionni
We study a generalization of the Harish-Chandra - Itzykson - Zuber integral to tensors and its expansion over trace-invariants of the two external tensors. This gives rise to natur…
Iterated foldings of discrete spaces and their limits: candidates for the role of Brownian map in higher dimensions
Luca Lionni, Jean-François Marckert
In this last decade, an important stochastic model emerged: the Brownian map. It is the limit of various models of random combinatorial maps after rescaling: it is a random metric…
A random matrix model with non-pairwise contracted indices
Luca Lionni, Naoki Sasakura
We consider a random matrix model with both pairwise and non-pairwise contracted indices. The partition function of the matrix model is similar to that appearing in some replicated…
Combinatorial study of graphs arising from the Sachdev-Ye-Kitaev model
Éric Fusy, Luca Lionni, Adrian Tanasa
We consider the graphs involved in the theoretical physics model known as the colored Sachdev-Ye-Kitaev (SYK) model. We study in detail their combinatorial properties at any order…
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…
On the joint distribution of the marginals of multipartite random quantum states
Stephane Dartois, Luca Lionni, Ion Nechita
We study the joint distribution of the set of all marginals of a random Wishart matrix acting on a tensor product Hilbert space. We compute the limiting free mixed cumulants of the…
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…
Multi-critical behaviour of 4-dimensional tensor models up to order 6
Luca Lionni, Johannes Thürigen
Tensor models generalize the matrix-model approach to 2-dimensional quantum gravity to higher dimensions. Some models allowing a expansion have been explored, most of them ge…
Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
Valentin Bonzom, Luca Lionni, Adrian Tanasa
The Sachdev-Ye-Kitaev (SYK) model is a model of interacting fermions. Gross and Rosenhaus have proposed a generalization of the SYK model which involves fermions with different…
Counting gluings of octahedra
Valentin Bonzom, Luca Lionni
Three--dimensional colored triangulations are gluings of tetrahedra whose faces carry the colors 0, 1, 2, 3 and in which the attaching maps between tetrahedra are defined using the…
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…
Colored triangulations of arbitrary dimensions are stuffed Walsh maps
Valentin Bonzom, Luca Lionni, Vincent Rivasseau
Regular edge-colored graphs encode colored triangulations of pseudo-manifolds. Here we study families of edge-colored graphs built from a finite but arbitrary set of building block…
Thermophysical properties of near-Earth asteroid (341843) 2008 EV5 from WISE data
V. Alí-Lagoa, L. Lionni, M. Delbo +3
Aims. To derive the thermal inertia of 2008 EV, the baseline target for the Marco Polo-R mission proposal, and infer information about the size of the particles on its surface.…