Related papers: Normal random matrix ensemble as a growth problem
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
We consider an inference on the eigenvalues of the covariance matrix of a multivariate normal distribution. The family of multivariate normal distributions with a fixed mean is seen as a Riemannian manifold with Fisher information metric.…
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…
Starting with a quaternion difference equation with boundary conditions, a parameterized sequence which is complete in finite dimensional quaternion Hilbert space is derived. By employing the parameterized sequence as the kernel of discrete…
We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the vibron model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results…
We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…
We derive general evolution equations describing the ensemble-average quantum dynamics generated by disordered Hamiltonians. The disorder average affects the coherence of the evolution and can be accounted for by suitably tailored effective…
Motivated by the importance ascribed to correlations in random matrices used to model phenomena in various scientific disciplines, we report how algebraic correlations between matrix elements affect the eigenvalue statistics and spectral…
We study the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter acting on growth and fragmentation. To this aim, we use the probabilistic individual-based interpretation of…
The role of the normalized modularity matrix in finding homogeneous cuts will be presented. We also discuss the testability of the structural eigenvalues and that of the subspace spanned by the corresponding eigenvectors of this matrix. In…
In this paper we describe a strategy to study the Anderson model of an electron in a random potential at weak coupling by a renormalization group analysis. There is an interesting technical analogy between this problem and the theory of…
Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and…
We study the semigroup of the symmetric $\alpha$-stable process in bounded domains in $\R^2$. We obtain a variational formula for the spectral gap, i.e. the difference between two first eigenvalues of the generator of this semigroup. This…
We study an "inner-product kernel" random matrix model, whose empirical spectral distribution was shown by Xiuyuan Cheng and Amit Singer to converge to a deterministic measure in the large $n$ and $p$ limit. We provide an interpretation of…
Spectral properties of random matrices play an important role in statistics, machine learning, communications, and many other areas. Engaging results regarding the convergence of the empirical spectral distribution (ESD) and the…
In this article, we are going to introduce the weighted numerical range which is a further generalization both the c-numerical range and the rank k numerical range. If the boundaries of weighted numerical ranges of two matrices (possibly of…
We study eigenvalues of general scalar Dirichlet polyharmonic problems in domains in $\mathbb R^{d}$. We first prove a number of inequalities satisfied by the eigenvalues on general domains, depending on the relations between the orders of…
Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous…
Algebraic domains are regions in the plane surrounded by mutually disjoint non-singular real algebraic curves. Poincar'e-Reeb Graphs of them are graphs they naturally collapse: such graphs are formally formulated by Sorea, for example,…