Related papers: Analysis of singular subspaces under random pertur…
In this paper, we study a class of equations representing nonlinear diffusion on networks. A particular instance of our model can be seen as a network equivalent of the porous-medium equation. We are interested in studying perturbations of…
Stability analysis of the Kalman filter under randomly lost measurements has been widely studied. We revisit this problem in a general continuous-time framework, where both the measurement matrix and noise covariance evolve as random…
This work discusses scalar-tensor theories of gravity, with a focus on the Brans-Dicke subclass, and one that also takes note of the latter's equivalence with $f(R)$ gravitation theories. A 1+3 covariant formalism is used in this case to…
We investigate a fully discrete finite element approximation for the stochastic Kuramoto-Sivashinsky equation, combining the standard finite element methods in spatial discretization with the implicit Euler-Maruyama scheme in time. Rigorous…
In this paper, we study the singularly perturbed Gaussian unitary ensembles defined by the measure \begin{equation*} \frac{1}{C_n} e^{- n\textrm{tr}\, V(M;\lambda,\vec{t}\;)}dM, \end{equation*} over the space of $n \times n$ Hermitian…
We discretize the stochastic Allen-Cahn equation with additive noise by means of a spectral Galerkin method in space and a tamed version of the exponential Euler method in time. The resulting error bounds are analyzed for the…
Computing the distribution of permanents of random matrices has been an outstanding open problem for several decades. In quantum computing, "anti-concentration" of this distribution is an unproven input for the proof of hardness of the task…
We study essentially bounded quantum random variables and show that the Gelfand spectrum of such a quantum random variable coincides with the hypoconvex hull of its essential range. Moreover, a notion of operator-valued variance is…
We study the eigenvector mass distribution for generalized Wigner matrices on a set of coordinates $I$, where $N^\varepsilon \le | I | \le N^{1- \varepsilon}$, and prove it converges to a Gaussian at every energy level, including the edge,…
In this paper we study the evolution of cosmological perturbations through a nonsingular bouncing universe using covariant perturbation theory and examine the validity of linear perturbation theory. The bounce is modeled by a two component…
We study the properties of singular values of mixing matrices embedded within an experimentally determined interval matrix. We argue that any physically admissible mixing matrix needs to have the property of being a contraction. This…
We consider the problem of approximating a $d \times d$ covariance matrix $M$ with a rank-$k$ matrix under $(\varepsilon,\delta)$-differential privacy. We present and analyze a complex variant of the Gaussian mechanism and obtain upper…
In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…
We consider the estimation of an n-dimensional vector s from the noisy element-wise measurements of $\mathbf{s}\mathbf{s}^T$, a generic problem that arises in statistics and machine learning. We study a mismatched Bayesian inference…
This paper explores the fundamental limits of a simple system, inspired by the intermittent Kalman filtering model, where the actuation direction is drawn uniformly from the unit hypersphere. The model allows us to focus on a fundamental…
We study a universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies and their groups and clusters) and two sets of perfect fluids with linear and nonlinear equations of state, respectively. The…
We extend the recently developed discrete geometric singular perturbation theory to the non-normally hyperbolic regime. Our primary tool is the Takens embedding theorem, which provides a means of approximating the dynamics of particular…
Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…
We study the stochastic nonlinear Schroedinger equations with linear multiplicative noise, particularly in the defocusing mass-critical and energy-critical cases. For general initial data, we prove the global existence and uniqueness of…
We study the statistical decision process of detecting the signal from a `signal+noise' type matrix model with an additive Wigner noise. We propose a hypothesis test based on the linear spectral statistics of the data matrix, which does not…