Related papers: Strong convergence for tensor GUE random matrices
We show that scalar quantum field theory in four Euclidean dimensions with global $O(N)^3$ symmetry and imaginary tetrahedral coupling is asymptotically free and bounded from below in the large-N limit. While the Hamiltonian is…
In random cellular systems, both observation and maximum entropy inference give a specific form to the topological pair correlation: it is bi-affine in the cells number of edges with coefficients depending on the distance between the two…
The Peterson-Thom conjecture asserts that any diffuse, amenable subalgebra of a free group factor is contained in a unique maximal amenable subalgebra. This conjecture is motivated by related results in Popa's deformation/rigidity theory…
We analyze the entanglement properties of the asymptotic steady state after a quench from free to hard-core bosons in one dimension. The R\'enyi and von Neumann entanglement entropies are found to be extensive, and the latter coincides with…
The dipole approximation is usually employed to describe light-matter interactions under ordinary conditions. With the development of artificial atomic systems, `giant atom' physics is possible, where the scale of atoms is comparable to or…
We study fundamental groups of clique complexes associated to random graphs. We establish thresholds for their cohomological and geometric dimension and torsion. We also show that in certain regime any aspherical subcomplex of a random…
We study asymptotics of representations of the unitary groups U(n) in the limit as n tends to infinity and we show that in many aspects they behave like large random matrices. In particular, we prove that the highest weight of a random…
We consider the general spin-1 SU(2) invariant Heisenberg model with a two-body interaction. A random loop model is introduced and relations to quantum spin systems is proved. Using this relation it is shown that for dimensions 3 and above…
Tensor products usually have nonzero torsion. This is a central theme of Auslander's paper "Modules over unramified regular local rings"; the theme continues in the work of Huneke and Wiegand. The main focus in this note is on tensor powers…
In this article we establish the arithmetic purity of strong approximation for certain semi-simple simply connected $k$-simple linear algebraic groups and their homogeneous spaces over a number field $k$. For instance, for any such group…
This paper generalizes former works of Derksen, Weyman and Zelevinsky about quivers with potentials. We consider semisimple finite-dimensional algebras $E$ over a field $F$, such that $E \otimes_{F} E^{op}$ is semisimple. We assume that $E$…
An action for a massless graviton interacting with a massive tensor field is proposed. The model is based on coupling the metric tensor to an SP(4) gauge theory spontaneously broken to $SL(2,C)$. The symmetry breaking is achieved by using a…
In this paper, we prove that in small parameter regions, arbitrary unitary matrix integrals converge in the large $N$ limit and match their formal expansion. Secondly we give a combinatorial model for our matrix integral asymptotics and…
The ground states of all even-even nuclei have angular momentum, $I$, equal to zero, I=0, and positive parity, $\pi=+$. This feature was believed to be a consequence of the attractive short-range interaction between nucleons. However, in…
We develop a quantum field-theoretic model of gravitationally induced entanglement (GIE) between two massive objects in spatial superposition. The masses are described as excitations of a scalar field in an external harmonic potential,…
Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the…
We prove a rigidity theorem that shows that, under many circumstances, quasi-isometric embeddings of equal rank, higher rank symmetric spaces are close to isometric embeddings. We also produce some surprising examples of quasi-isometric…
We extend the recent study of the k-body embedded Gaussian ensembles by Benet et al. (Phys. Rev. Lett. 87 (2001) 101601-1 and Ann. Phys. 292 (2001) 67) and by Asaga et al. (cond-mat/0107363 and cond-mat/ 0107364). We show that central…
We present a tensor-network approach for the strong-coupling expansion of two-dimensional QCD with staggered quarks at non-zero chemical potential. After expanding the Boltzmann factor in the gauge and fermion actions, all gauge fields can…
We give a unified treatment of the convergence of random series and the rate of convergence of strong law of large numbers in the framework of game-theoretic probability of Shafer and Vovk (2001). We consider games with the quadratic hedge…