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We extend the construction principle of multivariate phase-type distributions to establish an analytically tractable class of heavy-tailed multivariate random variables whose marginal distributions are of Mittag-Leffler type with arbitrary…
A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient…
The dynamics of distributed sources is described by nonlinear partial differential equations. Lagrangian analytical solutions of these (and associated) equations are obtained and discussed in the context of Lagrangian modeling - from the…
We propose new generalized multivariate hypergeometric distributions, which extremely resemble the classical multivariate hypergeometric distributions. The proposed distributions are derived based on an urn model approach. In contrast to…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
Recently, we developed a theory of a geometrically growing system. Here we show that the theory can explain some phenomena of power-law distribution including classical demographic and economic and novel pandemic instances, without…
This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the…
Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
The general limit distributions of the sum of random variables described by a finite matrix product ansatz are characterized. Using a mapping to a Hidden Markov Chain formalism, non-standard limit distributions are obtained, and related to…
Mixture quality plays a crucial role in the physical properties of multi-component immiscible polymer mixtures including nanocomposites and polymer blends. Such complex mixtures are often characterized by hierarchical internal structures,…
The_commuting variety_ is the pairs of NxN matrices (X,Y) such that XY = YX. We introduce the_diagonal commutator scheme_, {(X,Y) : XY-YX is diagonal}, which we prove to be a reduced complete intersection, one component of which is the…
We study the overlaps between right and left eigenvectors for random matrices of the spherical and truncated unitary ensembles. Conditionally on all eigenvalues, diagonal overlaps are shown to be distributed as a product of independent…
The distribution of the consecutive level-spacing ratio is now widely used as a tool to distinguish integrable from chaotic quantum spectra, mostly due to its avoiding of the numerical spectral unfolding. Similar to the use of the…
A mixed multigraph is obtained from an undirected multigraph by orienting a subset of its edges. In this paper, we study a new Hermitian matrix representation of mixed multigraphs, give an introduction to cospectral operations on mixed…
Quantum graphs can be extended to scattering systems when they are connected by leads to infinity. It is shown that for certain extensions, the scattering matrices of isospectral graphs are conjugate to each other and their poles…
We compute the joint distributions of arbitrary numbers of eigenvectors of real and complex symmetric random tensors by the quantum field theoretical methods which were previously used to compute the mean distributions. We obtain the random…
Moderately large numbers of transitive elliptic spreads are constructed in characteristic $2$ and dimension $\equiv $ 2 (mod 4).
We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term distributive homology and show…
We develop variation formulas for the quantities of extrinsic geometry for adapted variations of metrics on almost-product (e.g. foliated) Riemannian manifolds, and apply them to study the total mixed scalar curvature of a distribution --…