The Sk\mathfrak S_k-circular limit of random tensor flattenings

The tensor flattenings appear naturally in quantum information when one produces a density matrix by partially tracing the degrees of freedom of a pure quantum state. In this paper, we study the joint $^*$-distribution of the flattenings of large random tensors under mild assumptions, in the sense of free probability theory. We show the convergence toward an operator-valued circular system with amalgamation on permutation group algebras for which we describe the covariance structure. As an application we describe the law of large random density matrix of bosonic quantum states

From a consortium sequence to a unified sequence: the Bacillus subtilis 168 reference genome a decade later

Comparative genomics is the cornerstone of identification of gene functions. The immense number of living organisms precludes experimental identification of functions except in a handful of model organisms. The bacterial domain is split into large branches, among which the Firmicutes occupy a considerable space. Bacillus subtilis has been the model of Firmicutes for decades and its genome has been a reference for more than 10 years. Sequencing the genome involved more than 30 laboratories, with different expertises, in a attempt to make the most of the experimental information that could be associated with the sequence. This had the expected drawback that the sequencing expertise was quite varied among the groups involved, especially at a time when sequencing genomes was extremely hard work. The recent development of very efficient, fast and accurate sequencing techniques, in parallel with the development of high-level annotation platforms, motivated the present resequencing work. The updated sequence has been reannotated in agreement with the UniProt protein knowledge base, keeping in perspective the split between the paleome (genes necessary for sustaining and perpetuating life) and the cenome (genes required for occupation of a niche, suggesting here that B. subtilis is an epiphyte). This should permit investigators to make reliable inferences to prepare validation experiments in a variety of domains of bacterial growth and development as well as build up accurate phylogenies

The Sk\mathfrak S_k-circular limit of random tensor flattenings

International audienceThe tensor flattenings appear naturally in quantum information when one produces a density matrix by partially tracing the degrees of freedom of a pure quantum state. In this paper, we study the joint $^*$-distribution of the flattenings of large random tensors under mild assumptions, in the sense of free probability theory. We show the convergence toward an operator-valued circular system with amalgamation on permutation group algebras for which we describe the covariance structure. As an application we describe the law of large random density matrix of bosonic quantum states

The Sk\mathfrak S_k-circular limit of random tensor flattenings

International audienceThe tensor flattenings appear naturally in quantum information when one produces a density matrix by partially tracing the degrees of freedom of a pure quantum state. In this paper, we study the joint $^*$-distribution of the flattenings of large random tensors under mild assumptions, in the sense of free probability theory. We show the convergence toward an operator-valued circular system with amalgamation on permutation group algebras for which we describe the covariance structure. As an application we describe the law of large random density matrix of bosonic quantum states

The Sk\mathfrak S_k-circular limit of random tensor flattenings

The tensor flattenings appear naturally in quantum information when one produces a density matrix by partially tracing the degrees of freedom of a pure quantum state. In this paper, we study the joint $^*$-distribution of the flattenings of large random tensors under mild assumptions, in the sense of free probability theory. We show the convergence toward an operator-valued circular system with amalgamation on permutation group algebras for which we describe the covariance structure. As an application we describe the law of large random density matrix of bosonic quantum states

Conformality of 1/N1/N corrections in Sachdev-Ye-Kitaev-like models

International audienceThe Sachdev-Ye-Kitaev (SYK) model is a quantum-mechanical model of N Majorana fermions which displays a number of appealing features—solvability in the strong coupling regime, near-conformal invariance and maximal chaos—which make it a suitable model for black holes in the context of the AdS/CFT holography. In this paper, we show for the colored SYK model and several of its tensor model cousins that the next-to-leading order in the large-N expansion preserves the conformal invariance of the two-point function in the strong-coupling regime, up to the contribution of the pseudo-Goldstone bosons due to the explicit breaking of the symmetry which are already seen in the leading-order four-point function. We also comment on the composite field approach for computing correlation functions in colored tensor models