Related papers: A quantitative averaging lemma for spatially depen…
We prove a quantitative version of Oppenheim's conjecture for generic ternary indefinite quadratic forms. Our results are inspired by and analogous to recent results for diagonal quadratic forms due to Bourgain.
In this paper, we explain a simple and uniform construction of a smooth integral model associated to a quadratic, (anti)-hermitian, and (anti)-quaternionic hermitian lattice defined over an arbitrary local field. As one major application,…
Single index model is a powerful yet simple model, widely used in statistics, machine learning, and other scientific fields. It models the regression function as $g(<a,x>)$, where a is an unknown index vector and x are the features. This…
In this article, we demonstrate the common fixed point theorems for three transformations on vector S-metric space by utilizing weakly compatible and point of coincidence. Moreover, some of our results generalize the existing results in the…
In this paper, we prove a semistable reduction type theorem for multi-filtered vector spaces (or known as multi-weighted vector spaces).
We prove an intermediate value theorem of an arithmetical flavor, involving the consecutive averages of sequences with terms in a given finite set A. For every such set we completely characterize the numbers x ("intermediate values") with…
We establish a non-Archimedean analogue of Koksma's theorem. For a local field F of characteristic zero, we prove that the sequence ([{\alpha}x^n]) is uniformly distributed in the valuation ring O for almost every x with |x|_p>1. In the…
We herein establish an asymptotic representation theorem for locally asymptotically normal quantum statistical models. This theorem enables us to study the asymptotic efficiency of quantum estimators such as quantum regular estimators and…
The main result of this paper is a quantified version of Ingham's Tauberian theorem for bounded vector-valued sequences rather than functions. It gives an estimate on the rate of decay of such a sequence in terms of the behaviour of a…
The general notion of a Hausdorff-type operator with a kernel depending on an external variable is introduced and generalizations and analogs of classical results on the regularity of various summation methods are proved for the case of…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
We give two proofs of the Kalman Theorem, alternative to the most common ones, which infer such a classical result of Control Theory using just very basic facts on flows of vector fields. These proofs are apt to be generalised in diverse…
Conditional copula models allow dependence structures to vary with observed covariates while preserving a separation between marginal behavior and association. We study the uniform asymptotic behavior of kernel-weighted local likelihood…
The framework of locally covariant quantum field theory, an axiomatic approach to quantum field theory in curved spacetime, is reviewed. As a specific focus, the connection between spin and statistics is examined in this context. A new…
Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…
A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…
We show an analogue of the Klain-Schneider theorem for valuations that are invariant under rotations around a fixed axis, called zonal. Using this, we establish a new integral representation of zonal valuations involving mixed area measures…
A regularity lemma for polynomials provides a decomposition in terms of a bounded number of approximately independent polynomials. Such regularity lemmas play an important role in numerous results, yet suffer from the familiar shortcoming…
We prove a version of the reduction principle for functionals of vector long-range dependent random fields. The components of the fields may have different long-range dependent behaviours. The results are illustrated by an application to…
We prove a variant of the abstract probabilistic version of Szemer\'edi's regularity lemma, due to Tao, which applies to a number of structures (including graphs, hypergraphs, hypercubes, graphons, and many more) and works for random…