Related papers: Random Matrices and Holographic Tensor Models
A holographic dual description of inhomogeneous systems is discussed. Notably, finite temperature results for the entanglement entropy in both the rainbow chain and the SSD model are obtained holographically by choosing appropriate…
A new set of exact scattering matrices in 1+1 dimensions is proposed by solving the bootstrap equations. Extending earlier constructions of colour valued scattering matrices this new set has its colour structure associated to non…
We show the emergence of random matrix theory (RMT) spectral correlations in the chaotic phase of generic periodically kicked interacting quantum many-body systems by analytically calculating spectral form factor (SFF), $K(t)$, up to two…
We initiate the study of how tensor networks reproduce properties of static holographic space-times, which are not locally pure anti-de Sitter. We consider geometries that are holographically dual to ground states of defect, interface and…
We consider non-Hermitian random matrices $X \in \mathbb{C}^{n \times n}$ with general decaying correlations between their entries. For large $n$, the empirical spectral distribution is well approximated by a deterministic density,…
We analyze the density of roots of random polynomials where each complex coefficient is constructed of a random modulus and a fixed, deterministic phase. The density of roots is shown to possess a singular component only in the case for…
Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix…
The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$,…
Spontaneous symmetry breaking is well understood through the classical "Mexican Hat" picture, which describes many quantum phases of matter. Recently, several new classes of quantum phases of matter, such as topological orders and symmetry…
In a recent series of papers, a duality between orthogonal and symplectic random tensor models has been proven, first for quartic models and then for models with interactions of arbitrary order. However, the tensor models considered so far…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
We analyse non-local rotating observables in holography corresponding to spinning bound states. To renormalize their energies and momenta we suggest and discuss different holographic renormalization schemes motivated by the static non-local…
Orthogonal - unitary and symplectic - unitary crossover ensembles of random matrices are relevant in many contexts, especially in the study of time reversal symmetry breaking in quantum chaotic systems. Using skew-orthogonal polynomials we…
$O(N)$ invariants are the observables of real tensor models. We use regular colored graphs to represent these invariants, the valence of the vertices of the graphs relates to the tensor rank. We enumerate $O(N)$ invariants as $d$-regular…
The prevalence of hidden Markov models (HMMs) in various applications of statistical signal processing and communications is a testament to the power and flexibility of the model. In this paper, we link the identifiability problem with…
We show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer algebras. These algebras are shown to be semi-simple and their Wedderburn-Artin…
We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminium plate may have an…
Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…