Related papers: Random Matrix Theory by the Supersymmetry Method B…
We study the sine-Gordon (SG) model at finite densities of the topological charge and small SG interaction constant, related to the one-dimensional Hubbard model near half-filling. Using the modified WKB approach, we find that the spectrum…
A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations in ensembles of random vector-valued variables, is proposed. This route is completely different from the additive mechanism…
We revisit the smooth convex-concave bilinearly-coupled saddle-point problem of the form $\min_x\max_y f(x) + \langle y,\mathbf{B} x\rangle - g(y)$. In the highly specific case where each of the functions $f(x)$ and $g(y)$ is either affine…
We propose a novel approach to the analysis of experimental data obtained in relativistic nucleus-nucleus collisions which borrows from methods developed within the context of Random Matrix Theory. It is applied to the detection of…
We formally extend the energy landscape approach for the thermodynamics of liquids to account for saddle points. By considering the extensive nature of macroscopic potential energies, we derive the scaling behavior of saddles with system…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
The energy landscape of multiverse cosmology is often modeled by a multi-dimensional random Gaussian potential. The physical predictions of such models crucially depend on the eigenvalue distribution of the Hessian matrix at potential…
This paper investigates the predictive performance of model averaging in high-dimensional linear regression where the number of regressors is comparable to the sample size. We demonstrate that the double descent trajectory manifests within…
Dark matter and dark energy are usually assumed to couple only gravitationally. An extension to this picture is to model dark energy as a scalar field coupled directly to cold dark matter. This coupling leads to new physical effects, such…
In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing…
Maximally supersymmetric gauge theories have experienced renewed interest due to the AdS/CFT correspondence and its conjectured S-duality. These gauge theories possess a large amount of symmetry and have quasi-integrable properties. We…
This work presents a mathematical treatment of the relation between Self-Organizing Maps (SOMs) and Gaussian Mixture Models (GMMs). We show that energy-based SOM models can be interpreted as performing gradient descent, minimizing an…
1. A standard Gaussian random matrix has full rank with probability 1 and is well-conditioned with a probability quite close to 1 and converging to 1 fast as the matrix deviates from square shape and becomes more rectangular. 2. If we…
Uniform semiclassical approximations for the number and kinetic-energy densities are derived for many non-interacting fermions in one-dimensional potentials with two turning points. The resulting simple, closed-form expressions contain the…
One of the main problems of observational cosmology is to determine the range in which a reliable measurement of galaxy correlations is possible. This corresponds to determine the shape of the correlation function, its possible evolution…
We investigate the impact of limited data on training pairwise energy-based models for inverse problems aimed at identifying interaction networks. Utilizing the Gaussian model as testbed, we dissect training trajectories across the…
Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard-Stratonovich transformation. Here, we complete this extension by including arbitrary…
We derive an analytic expression for the two-point correlation function in redshift space which (i) is nonlinear; (ii) is valid on the full sky, i.e. the distant-observer limit is not assumed; (iii) can account for the effect of…
Recent advances in the calculation of the $b\to s\gamma$ decay branching ratio are presented in the context of supersymmetric theories. Theoretical accuracy increased by inclusion of the next-to-leading order QCD corrections makes it…
Robustness, domain adaptation, photometric/occlusion invariance, sensor drift, and alignment style are treated as separate literatures with separate method families. Under label-preserving deployment shift they share one geometric object:…