Related papers: The "north pole problem" and random orthogonal mat…
For fixed $m>1$, we consider $m$ independent $n \times n$ non-Hermitian random matrices $X_1, ..., X_m$ with i.i.d. centered entries with a finite $(2+\eta)$-th moment, $ \eta>0.$ As $n$ tends to infinity, we show that the empirical…
We study the distribution of entries of a random permutation matrix under a "randomized basis," i.e., we conjugate the random permutation matrix by an independent random orthogonal matrix drawn from Haar measure. It is shown that under…
Suppose $X$ is a finite discrete space with at least two elements, $\Gamma$ is a nonempty countable set, and consider self--map $\varphi:\Gamma\to\Gamma$. We prove that the generalized shift $\sigma_\varphi:X^\Gamma\to X^\Gamma$ with…
The segment distribution around the center of gravity is investigated for a special comb polymer (triangular polymer) having the side chains of the same generation number, $g$, as the main backbone. Common to all the other polymers, the…
There is renewed attention to whether we can observe the decoherence effect in neutrino oscillation due to the separation of wave packets with different masses in near-future experiments. As a contribution to this endeavor, we extend the…
We show that a classical uniformly distributed phenomenon for an element and its inverse in ($\mathbb{Z}/n\mathbb{Z})^{*}$ also exists in $\textrm{GL}_{n}(\mathbb{F}_{p})$. A $\textrm{GL}_{n}(\mathbb{F}_{p})$ analogy of the uniform…
This paper is devoted to the Gaussian fluctuations and deviations of the traces of tridiagonal random matrix. Under quite general assumptions, we prove that the traces are approximately normal distributed. Multi-dimensional central limit…
Gaussian distributions can be generalized from Euclidean space to a wide class of Riemannian manifolds. Gaussian distributions on manifolds are harder to make use of in applications since the normalisation factors, which we will refer to as…
An integro-differential equation describing the angular distribution of beams is analyzed for a medium with random inhomogeneities. Beams are trapped because inhomogeneities give rise to wave localization at random locations and random…
We formulate and study an elliptic transmission-like problem combining local and nonlocal elements. Let $\mathbb{R}^{n}$ be separated into two components by a smooth hypersurface $\Gamma$. On one side of $\Gamma$, a function satisfies a…
This paper is concerned with a rate-distortion theory for sequences of i.i.d. random variables with general distribution supported on general sets including manifolds and fractal sets. Manifold structures are prevalent in data science,…
Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through…
Suppose X is a frequency vector that follows a central multiple hyper-geometric distribution, such as arises in random sampling of an m-category attribute from a finite population without replacement. We show that the probability that X…
Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…
This study examines the statistical nature of instantaneous scalar concentration in an elevated point-source plume (neutral or buoyant) dispersing within a turbulent boundary layer. Using high-frequency long-duration experimental…
With a graph $G=(V,E)$ we associate a collection of non-negative real weights $\cup_{v\in V}{\lambda_{i,v}:1\leq i \leq m} \cup \cup_{uv \in E} {\lambda_{ij,uv}:1\leq i \leq j \leq m}$. We consider the probability distribution on…
We suggest a new scenario in which the Universe starts its evolution with a fractal topological structure. This structure is described by a gas of wormholes. It is shown that the polarization of such a gas in external fields possesses a…
Most current pulsar emission models assume photon production and emission within the magnetosphere. Low frequency radiation is preferentially produced in the vicinity of the polar caps whereas the high-energy tail is shifted to regions…
The first part of the paper centers in the study of embeddability between partially commutative groups. In [KK], for a finite simplicial graph $\Gamma$, the authors introduce an infinite, locally infinite graph $\Gamma^e$, called the…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…