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We investigate a state discrimination problem in operationally the most general framework to use a probability, including both classical, quantum theories, and more. In this wide framework, introducing closely related family of ensembles…
Using tools from the theory of optimal transport, we establish several results concerning isometric actions of amenable topological groups with potentially unbounded orbits. Specifically, suppose $d$ is a compatible left-invariant metric on…
We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic…
The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong…
We survey a number of models from physics, statistical mechanics, probability theory and combinatorics, which are each described in terms of an orthogonal polynomial ensemble. The most prominent example is apparently the Hermite ensemble,…
We present a rigorous thermodynamic treatment of irreversible binary aggregation. We construct the Smoluchowski ensemble as the set of discrete finite distributions generated from the same initial state of all monomers upon fixed number…
We develop the formalism of universal torsors in equivariant birational geometry and apply it to produce new examples of nonbirational but stably birational actions of finite groups.
Ensembles improve prediction performance and allow uncertainty quantification by aggregating predictions from multiple models. In deep ensembling, the individual models are usually black box neural networks, or recently, partially…
In this paper, we study the Dvoretzky covering problem with non-uniformly distributed centers. When the probability law of the centers admits an absolutely continuous density which satisfies a regular condition on the set of essential…
We explore the role of group symmetries in binary classification tasks, presenting a novel framework that leverages the principles of Neyman-Pearson optimality. Contrary to the common intuition that larger symmetry groups lead to improved…
Let $X$ be a symmetric, isotropic random vector in $\mathbb{R}^m$ and let $X_1...,X_n$ be independent copies of $X$. We show that under mild assumptions on $\|X\|_2$ (a suitable thin-shell bound) and on the tail-decay of the marginals…
We develop a relativistic framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the…
Random matrix theory has proven very successful in the understanding of the spectra of chaotic systems. Depending on symmetry with respect to time reversal and the presence or absence of a spin 1/2 there are three ensembles, the Gaussian…
Equilibrium Statistical Mechanics is undoubtedly a cornerstone for the description of many particle systems. The common interpretation is based on ensemble theory as put forward by Gibbs, alongside the basic assumptions that different…
This article is intended to provide a pedagogical introduction to the supersymmetry method for performing ensemble-averaging in Gaussian random-matrix theory. The method is illustrated by a detailed calculation of the simplest non-trivial…
The maximal regularity property of discontinuous Galerkin methods for linear parabolic equations is used together with variational techniques to establish a priori and a posteriori error estimates of optimal order under optimal regularity…
In this paper we construct optimal designs for frequentist model averaging estimation. We derive the asymptotic distribution of the model averaging estimate with fixed weights in the case where the competing models are non-nested and none…
We prove a normal form theorem for Poisson structures around Poisson transversals (also called cosymplectic submanifolds), which simultaneously generalizes Weinstein's symplectic neighborhood theorem from symplectic geometry and Weinstein's…
The spherical ensemble is a well-known ensemble of N repulsive points on the two-dimensional sphere, which can realized in various ways (as a random matrix ensemble, a determinantal point process, a Coulomb gas, a Quantum Hall state...).…
In this paper, we prove a new ergodic theorem for $\mathbb{R}^d$-actions involving averages over dilated submanifolds, thereby generalizing the theory of spherical averages. Our main result is a quantitative estimate for the error term of…