Related papers: Geometrical and spectral study of $\beta$-skeleton…
We study the edge overlap and local limit of the random spanning tree in random environment (RSTRE) on the complete graph with $n$ vertices and weights given by $\exp(-\beta \omega_e)$ for $\omega_e$ uniformly distributed on $[0,1]$. We…
Quite often real-world networks can be thought of as being symmetric, in the abstract sense that vertices can be found to have similar or equivalent structural roles. However, traditional measures of symmetry in graphs are based on their…
In the present work, we have done a systematic study of beta decay properties such as electron spectral-shapes, shape factors, and log$ft$ values for the higher forbidden non-unique $\beta^{-}$ transitions in the mass region A=85-123. We…
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
We study regular graphs whose distance-$2$ graph or distance-$1$-or-$2$ graph is strongly regular. We provide a characterization of such graphs $\Gamma$ (among regular graphs with few distinct eigenvalues) in terms of the spectrum and the…
Statistical field theory methods have been very successful with a number of random graph and random matrix problems, but it is challenging to apply these methods to graphs with prescribed degree sequences due to the extensive number of…
We calculate the parameters $\gamma$ and $\beta$ in the parametrized post-Newtonian (PPN) formalism for scalar-tensor gravity (STG) with an arbitrary potential, under the assumption that the source matter is given by a non-rotating sphere…
We use a multivariate central limit theorem (CLT) to study the distribution of random geometric graphs (RGGs) on the cube and torus in the high-dimensional limit with general node distributions. We find that the distribution of RGGs on the…
Random Matrix Theory (RMT) is capable of making predictions for the spectral fluctuations of a physical system only after removing the influence of the level density by unfolding the spectra. When the level density is known, unfolding is…
Let $\mathbf{B}_n=\mathbf {S}_n(\mathbf {S}_n+\alpha_n\mathbf {T}_N)^{-1}$, where $\mathbf {S}_n$ and $\mathbf {T}_N$ are two independent sample covariance matrices with dimension $p$ and sample sizes $n$ and $N$, respectively. This is the…
We explicitly quantify the empirically observed phenomenon that estimation under a stochastic block model (SBM) is hard if the model contains classes that are similar. More precisely, we consider estimation of certain functionals of random…
Random Matrix Theory (RMT) has successfully modeled diverse systems, from energy levels of heavy nuclei to zeros of $L$-functions. Many statistics in one can be interpreted in terms of quantities of the other; for example, zeros of…
We present an analysis of the spectral density of the adjacency matrix of large random trees. We show that there is an infinity of delta peaks at all real numbers which are eigenvalues of finite trees. By exact enumerations and Monte-Carlo…
The spectral properties of the spinless fermion model with nearest-neighbor repulsive interactions on a one-dimensional lattice are investigated using the Bethe ansatz. Although its bulk quantities are exactly the same as those of the…
In recent work on equiangular lines, Jiang, Tidor, Yuan, Zhang, and Zhao showed that a connected bounded degree graph has sublinear second eigenvalue multiplicity. More generally they show that there cannot be too many eigenvalues near the…
Model-based analysis tools, built on assumptions and simplifications, are difficult to handle smart grids with data characterized by 4Vs data. This paper, using random matrix theory (RMT), motivates data-driven tools to perceive the complex…
The schematic model of interacting spins is introduced, which combines the symmetry of hypercube with the simplicity of random regular graph with degree three, i.e. the random cubic graph. We study the localization transition in this model,…
The paper studies scaling limits of random skew plane partitions confined to a box when the inner shapes converge uniformly to a piecewise linear function V of arbitrary slopes in [-1,1]. It is shown that the correlation kernels in the bulk…
Regional data analysis is concerned with the analysis and modeling of measurements that are spatially separated by specifically accounting for typical features of such data. Namely, measurements in close proximity tend to be more similar…