Related papers: Level Repulsion in Constrained Gaussian Random-Mat…
The probability distribution of the closest neighbor and farther neighbor spacings from a given level have been studied for interacting fermion/boson systems with and without spin degree of freedom constructed using an embedded GOE of one…
Generalized linear mixed models (GLMMs) are a widely used tool in statistical analysis. The main bottleneck of many computational approaches lies in the inversion of the high dimensional precision matrices associated with the random…
Observables in random tensor theory are polynomials in the entries of a tensor of rank $d$ which are invariant under $U(N)^d$. It is notoriously difficult to evaluate the expectations of such polynomials, even in the Gaussian distribution.…
Three recently suggested random matrix ensembles (RME) are linked together by an exact mapping and plausible conjections. Since it is known that in one of these ensembles the eigenvector statistics is multifractal, we argue that all three…
This article concerns a class of generalized linear mixed models for clustered data, where the random effects are mapped uniquely onto the grouping structure and are independent between groups. We derive necessary and sufficient conditions…
Generalized Advantage Estimation (GAE) has been used to mitigate the computational complexity of reinforcement learning (RL) by employing an exponentially weighted estimation of the advantage function to reduce the variance in policy…
We prove that the persistence diagram of the sublevel set filtration of the quadratic form f(x) = x^T M x restricted to the unit sphere S^{n-1} is analytically determined by the eigenvalues of the symmetric matrix M. By Morse theory, the…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
For a set of distances D={d_1,...,d_k} a set A is called D-avoiding if no pair of points of A is at distance d_i for some i. We show that the density of A is exponentially small in k provided the ratios d_1/d_2, d_2/d_3, ..., d_{k-1}/d_k…
We study a class of $d$-dimensional random walks, including the two-dimensional simple random walk, reweighted by a self-repelling Gibbsian pair potential. We prove lower bounds on the diffusion constant for short-range interactions, and…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
Motivated by the simplicity and direct phenomenological applicability of field-theoretic orbifold constructions in the context of grand unification, we set out to survey the immensely rich group-theoretical possibilities open to this type…
We investigate ensemble methods for prediction in an online setting. Unlike all the literature in ensembling, for the first time, we introduce a new approach using a meta learner that effectively combines the base model predictions via…
In this paper, we employ variational arguments to establish a connection between ensemble methods for Neural Networks and Bayesian inference. We consider an ensemble-based scheme where each model/particle corresponds to a perturbation of…
Until now only for specific crossovers between Poissonian statistics (P), the statistics of a Gaussian orthogonal ensemble (GOE), or the statistics of a Gaussian unitary ensemble (GUE) analytical formulas for the level spacing distribution…
My dissertation revolves around Bayesian approaches towards constrained statistical inference in the factor analysis (FA) model. Two interconnected types of restricted-model selection are considered. These types have a natural connection to…
Unitary ensembles of large N x N random matrices with a non-Gaussian probability distribution P[H] ~ exp{-TrV[H]} are studied using a theory of polynomials orthogonal with respect to exponential weights. Asymptotically exact expressions for…
The energy levels of a quantum graph with time reversal symmetry and unidirectional classical dynamics are doubly degenerate and obey the spectral statistics of the Gaussian Unitary Ensemble. These degeneracies, however, are lifted when the…
We prove multi-dimensional central limit theorems for the spectral moments (of arbitrary degrees) associated with random matrices with real-valued i.i.d. entries, satisfying some appropriate moment conditions. Our techniques rely on a…
Error mitigation techniques, while instrumental in extending the capabilities of near-term quantum computers, often suffer from exponential resource scaling with noise levels. To address this limitation, we introduce a novel approach,…