Related papers: Uniform bounds for period integrals and sparse equ…
The generalized pseudospectral method is employed for the accurate calculation of eigenvalues, densities and expectation values for the spiked harmonic oscillators. This allows \emph{nonuniform} and \emph{optimal} spatial discretization of…
We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…
We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution…
We obtain an uniform tail estimates for natural normed sums of independent random variables (r.v.) with regular varying tails of distributions. We give also many examples on order to show the exactness of offered estimates and discuss some…
Let $\Gamma$ be a non-uniform lattice in $\operatorname{PSL}(2,\mathbb R)$. In this note, we show that there exists a constant $\gamma_0>0$ such that for any $0<\gamma<\gamma_0$, any one-parametrer unipotent subgroup $\{u(t)\}_{t\in\mathbb…
Spectral clustering is a fundamental method for graph partitioning, but its reliance on eigenvector computation limits scalability to massive graphs. Classical sparsification methods preserve spectral properties by sampling edges…
We present a spectral method for parabolic partial differential equations with zero Dirichlet boundary conditions. The region {\Omega} for the problem is assumed to be simply-connected and bounded, and its boundary is assumed to be a smooth…
Suppose that $(M,\mathfrak{g})$ is a compact Riemannian manifold with strictly negative sectional curvatures. A subset of conjugacy classes $E \subset \text{conj}(\pi_1(M))$ is called spectrally rigid if when two negatively curved…
We extend the spectral method for proving limit theorems to random non-uniformly expanding dynamical systems. This yields the CLT and moderate deviations principles (MDP). We show that as the amount of non-uniformity decreases the CLT rates…
Consider the partial sums {S_t} of a real-valued functional F(Phi(t)) of a Markov chain {Phi(t)} with values in a general state space. Assuming only that the Markov chain is geometrically ergodic and that the functional F is bounded, the…
This paper studies certain horocyclic orbits on $\Gamma(1)\frontslash\mathcal{H}$. In the first instance we examine horocycles defined using the pencil of circles whose common point (in the words of the Nielsen-Fenchel manuscript is…
We consider Bourgain's ergodic theorem regarding arithmetic averages in the cases where quantitative mixing is present in the dynamical system. Focusing on the case of the horocyclic flow, those estimates allows us to bound from above the…
We investigate the stationary distribution of asymmetric and weakly asymmetric simple exclusion processes with open boundaries. We project the stationary distribution onto a subinterval, whose size is allowed to grow with the length of the…
We calculate the mean and variance of sums of the M\"obius function and the indicator function of the squarefrees, in both short intervals and arithmetic progressions, in the context of the ring of polynomials over a finite field of $q$…
We study signals that are sparse in graph spectral domain and develop explicit algorithms to reconstruct the support set as well as partial components from samples on few vertices of the graph. The number of required samples is independent…
Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…
The distribution function of particles over clusters is proposed for a system of identical intersecting spheres, the centres of which are uniformly distributed in space. Consideration is based on the concept of the rank number of clusters,…
We prove effective equidistribution of non-closed horocycles in the unit tangent bundle of infinite-volume geometrically finite hyperbolic surfaces.
We prove an effective equidistribution theorem for semisimple closed orbits on compact adelic quotients. The obtained error depends polynomially on the minimal complexity of intermediate orbits and the complexity of the ambient space. The…
We consider random geometric graphs on the plane characterized by a non-uniform density of vertices. In particular, we introduce a graph model where $n$ vertices are independently distributed in the unit disc with positions, in polar…