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In this paper, we consider the transmission eigenvalue problem associated with a general conductive transmission condition and study the geometric structures of the transmission eigenfunctions. We prove that under a mild regularity…
We consider the empirical eigenvalue distribution of an $m\times m$ principal submatrix of an $n\times n$ random unitary matrix distributed according to Haar measure. For $n$ and $m$ large with $\frac{m}{n}=\alpha$, the empirical spectral…
Densifying networks and deploying more antennas at each access point are two principal ways to boost the capacity of wireless networks. However, the complicated distributions of the signal power and the accumulated interference power,…
McKay proved that the limiting spectral measures of the ensembles of $d$-regular graphs with $N$ vertices converge to Kesten's measure as $N\to\infty$. In this paper we explore the case of weighted graphs. More precisely, given a large…
This paper presents a tractable analytical framework for the exact calculation of probability of node isolation and minimum node degree distribution when $N$ sensor nodes are independently and uniformly distributed inside a finite square…
This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all…
We have analyzed the transmission properties of pulses through one-dimensional periodic structures in order to systematically explore the best conditions to achieve the maximum delay with the minimum possible distortion. In the absence of…
Modern wireless channels are increasingly dense and mobile making the channel highly non-stationary. The time-varying distribution and the existence of joint interference across multiple degrees of freedom (e.g., users, antennas, frequency…
We study random normal matrix models whose eigenvalues tend to be distributed within a narrow "band" around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials…
In line with Pomeau's conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes…
An undersampled point spread function may interact with the microstructure of a solid-state detector such that the total flux detected can depend sensitively on where the PSF center falls within a pixel. Such intra-pixel sensitivity…
This article investigates signal estimation in wireless transmission (i.e., receive combining) from the perspective of statistical machine learning, where the transmit signals may be from an integrated sensing and communication system; that…
Wireless transmitters (Txs) that radiate downward in a direction often generate circular footprints on the ground. The configurational flexibility of these footprints is inherently limited as coverage adjustments are restricted to…
In this work, we present a wireless localization method that operates on self-supervised and unlabeled channel estimates. Our self-supervising method learns general-purpose channel features robust to fading and system impairments. Learned…
The scaling theory of Anderson localization is based on a global conductance $g_L$ that remains a random variable of order O(1) at criticality. One realization of such a conductance is the Landauer transmission for many transverse channels.…
Wireless systems are getting deployed in many new environments with different antenna heights, frequency bands and multipath conditions. This has led to an increasing demand for more channel measurements to understand wireless propagation…
The distribution of the sum of 1-dependent lattice vectors with supports on coordinate axes is approximated by a multivariate compound Poisson distribution and by signed compound Poisson measure. The local and $\ell_\alpha$-norms are used…
Given a finitely generated amenable group we consider ergodic random Schr\"odinger operators on a Cayley graph with random potentials and random boundary conditions. We show that the normalised eigenvalue counting functions of finite volume…
We study a lattice model for the spreading of fluid films, which are a few molecular layers thick, in narrow channels with inert lateral walls. We focus on systems connected to two particle reservoirs at different chemical potentials,…
The main result of this paper is a bound on the distance between the distribution of an eigenfunction of the Laplacian on a compact Riemannian manifold and the Gaussian distribution. If $X$ is a random point on a manifold $M$ and $f$ is an…