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Parameter-dependent statistical properties of spectra of totally connected irregular quantum graphs with Neumann boundary conditions are studied. The autocorrelation functions of level velocities c(x) and c(w,x) as well as the distributions…
We explain how the spectral curve can be extracted from the ${\cal W}$-representation of a matrix model. It emerges from the part of the ${\cal W}$-operator, which is linear in time-variables. A possibility of extracting the spectral curve…
The study of dissipation and decoherence in generic open quantum systems recently led to the investigation of spectral and steady-state properties of random Lindbladian dynamics. A natural question is then how realistic and universal those…
The network density matrix formalism allows for describing the dynamics of information on top of complex structures and it has been successfully used to analyze from system's robustness to perturbations to coarse graining multilayer…
We analyze the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process on a finite lattice and with the most general open boundary conditions. We extend results obtained…
We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical…
We investigate the fluctuations of linear spectral statistics of a Wigner matrix $W\_N$ deformed by a deterministic diagonal perturbation $D\_N$, around a deterministic equivalent which can be expressed in terms of the free convolution…
We equip the edges of a deterministic graph $H$ with independent but not necessarily identically distributed weights and study a generalized version of matchings (i.e. a set of vertex disjoint edges) in $H$ satisfying the property that…
We investigate the addition of applied stress to a random block matrix model introduced by Parisi to study the Hessian matrix of soft spheres near the jamming point. In the infinite dimensional limit the applied stress translates the…
We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over…
We study some spectral properties of a matrix that is constructed as a combination of a Laplacian and an adjacency matrix of simple graphs. The matrix considered depends on a positive parameter, as such we consider the implications in…
The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of matrix entries.
We compute the spectral statistics of the sum H of two independent complex Wishart matrices, each of which is correlated with a different covariance matrix. Random matrix theory enjoys many applications including sums and products of random…
We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
We study stochastic graph optimization problems in a novel distributed setting. As in the standard centralized setting, a random subgraph $G^*$ of a known base graph $G$ is realized by including each edge $e$ independently with a known…
The eigendecomposition of the coupling matrix of large biological networks is central to the study of the dynamics of these networks. For neural networks, this matrix should reflect the topology of the network and conform with Dale's law…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…