Related papers: Spectral Independence in High-Dimensional Expander…
We study localization and derive stochastic estimates (in particular, Wegner and Minami estimates) for the eigenvalues of weakly correlated random discrete Schr\"odinger operators in the localized phase. We apply these results to obtain…
For a large class of symmetric random matrices with correlated entries, selected from stationary random fields of centered and square integrable variables, we show that the limiting distribution of eigenvalue counting measure always exists…
For discrete-time nonautonomous linear dynamics and a large class of discrete growth rates $\mu$, we show that the notion of $\mu$ dichotomy (with respect to a sequence of norms) can be completely characterized in terms of ordinary and…
In the current paper we consider a Wigner matrix and consider an analytic function of polynomial growth on a set containing the support of the semicircular law in its interior. We prove that the linear spectral statistics corresponding to…
We consider a sequence of matrices that are associated to Markov dynamical systems and use determinant-free linear algebra techniques (as well as some algebra and complex analysis) to rigorously estimate the eigenvalues of every matrix…
Motivated by possible applications of spectral singularities in optics, we develop a semiclassical method of computing spectral singularities. We use this method to examine the spectral singularities of a planar slab gain medium whose gain…
We study the local geometry of empirical risks in high dimensions via the spectral theory of their Hessian and information matrices. We focus on settings where the data, $(Y_\ell)_{\ell =1}^n \in \mathbb{R}^d$, are i.i.d. draws of a…
We study spectral properties of the self-affine measure $\mu_{M,\mathcal {D}}$ generated by an expanding integer matrix $M\in M_n(\mathbb{Z})$ and a consecutive collinear digit set $\mathcal {D}=\{0,1,\dots,q-1\}v$ where $v\in…
This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…
The spatial distribution of persistent (unvisited) sites in one dimensional $A+A\to\emptyset$ model is studied. The `empty interval distribution' $n(k,t)$, which is the probability that two consecutive persistent sites are separated by…
In this article we show the existence of limiting spectral distribution of a symmetric random matrix whose entries come from a stationary Gaussian process with covariances satisfying a summability condition. We provide an explicit…
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…
Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…
It is found that the total IMF-transverse-energy (E_t) spectra in multi-IMF events are well represented by synthetic spectra obtained by folding of the single-IMF spectrum. Using the experimental IMF multiplicity distribution, the observed…
We investigate joint spectral characteristics of a family of matrices $\mathcal F $, associated with products in the semigroup generated by $\mathcal F$. In the literature, extremal measures such as the well-known joint spectral radius and…
Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four…
Exponential random graphs are used extensively in the sociology literature. This model seeks to incorporate in random graphs the notion of reciprocity, that is, the larger than expected number of triangles and other small subgraphs.…
Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…
The $W$-random graphs provide a flexible framework for modeling large random networks. Using the Large Deviation Principle (LDP) for $W$-random graphs from [9], we prove the LDP for the corresponding class of random symmetric…
Recently, it was shown that the probability distribution function (PDF) of the free energy of a single continuum directed polymer (DP) in a random potential, equivalently of the height of a growing interface described by the…