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A stochastic method is introduced for geometric modeling aerosol surface roughness with random field and discrete differential geometry theory. Optical scattering properties are computed for randomly oriented spheroidal particles with…
Scattering of electromagnetic waves in billiard-like systems has become a standard experimental tool of studying properties associated with Quantum Chaos. Random Matrix Theory (RMT) describing statistics of eigenfrequencies and associated…
We consider a composite medium, which consists of a homogeneous matrix containing a statistically homogeneous set of multimodal spherical inclusions. This model is used to represent the morphology of heterogeneous solid propellants (HSP)…
We review models of random geometries based on the dynamical lattice approach. We discuss one dimensional model of simplicial complexes (branched polymers), two dimensional model of dynamical triangulations and four dimensional model of…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
We consider the efficiency of multiplexing spatially encoded information across random configurations of a metasurface-programmable chaotic cavity in the microwave domain. The distribution of the effective rank of the channel matrix is…
Matrix normal models have an associated 4-tensor for their covariance representation. The covariance array associated with a matrix normal model is naturally represented as a Kronecker-product structured covariance associated with the…
We define a message-passing algorithm for computing magnetizations in Restricted Boltzmann machines, which are Ising models on bipartite graphs introduced as neural network models for probability distributions over spin configurations. To…
In this article, we study microscopic properties of a two-dimensional eigenvalue ensemble near a conical singularity arising from insertion of a point charge in the bulk of the support of eigenvalues. In particular, we characterize all…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
In the last few years several new Random Matrix Models have been proposed and studied. They have found application in various different contexts, ranging from the physics of mesoscopic systems to the chiral transition in lattice gauge…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We study the matrix ansatz in the quantum group framework, applying integrable systems techniques to statistical physics models. We start by reviewing the two approaches, and then show how one can use the former to get new insight on the…
We study the entanglement spectrum of a translationally-invariant lattice system under a random partition, implemented by choosing each site to be in one subsystem with probability $p\in[0, 1]$. We apply this random partitioning to a…
We study properties of Hamiltonian integrable systems with random initial data by considering their Lax representation. Specifically, we investigate the spectral behaviour of the corresponding Lax matrices when the number $N$ of degrees of…
We introduce a concept for random tilings which, comprising the conventional one, is also applicable to tiling ensembles without height representation. In particular, we focus on the random tiling entropy as a function of the tile…
We introduce a numerical method that enables efficient modelling of light scattering by large, disordered ensembles of non-spherical particles incorporated in stratified media, including when the particles are in close vicinity to each…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
The partition function of the 2d Ising model with random nearest neighbor coupling is expressed in the dual lattice made of square plaquettes. The dual model is solved in the the mean field and in different types of Bethe-Peierls…
A restricted Boltzmann machine (RBM) is an undirected graphical model constructed for discrete or continuous random variables, with two layers, one hidden and one visible, and no conditional dependency within a layer. In recent years, RBMs…