Related papers: Ekeland's Variational Principle for An $\bar{L}^{0…
The main objective of this paper is to develop extreme value theory for $\vartheta$-expansions. We establish the limit distribution of the maximum value in a $\vartheta$-continued fraction mixing stationary stochastic process, along with…
Large deviation principles for hyperbolic systems are well studied and provide exponential rates for the deviations of Birkhoff averages from their limit. This short article presents a local large deviation principle for Smale spaces, in…
Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…
The aim of this paper is to study the asymptotic expansion in total variation in the Central Limit Theorem when the law of the basic random variable is locally lower-bounded by the Lebesgue measure (or equivalently, has an absolutely…
Via a symmetric version of Ekeland's principle recently obtained by the author we improve, in a ball or an annulus, a result of Boccardo-Ferone-Fusco-Orsina on the properties of minimizing sequences of functionals of calculus of variations…
We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may…
The simple L\'evy Poisson process and scaled forms are explicitly constructed from partial sums of independent and identically distributed random variables and from sums of non-stationary independent random variables. For the latter, the…
The Energy-Dissipation Principle provides a variational tool for the analysis of parabolic evolution problems: solutions are characterized as so-called null-minimizers of a global functional on entire trajectories. This variational…
The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic dynamics developed by the first author \textit{et al}. to establish quenched versions of the large deviation…
This article shows that counting or computing the small eigenvalues of the Witten Laplacian in the semi-classical limit can be done without assuming that the potential is a Morse function as the authors did in [LNV]. In connection with…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we show that functions of bounded variation (BV functions) can be approximated in the strict sense and pointwise uniformly by special…
A framework to boost the efficiency of Bayesian inference in probabilistic programs is introduced by embedding a sampler inside a variational posterior approximation. We call it the refined variational approximation. Its strength lies both…
We present a novel framework for variable selection in Fr\'echet regression with responses in general metric spaces, a setting increasingly relevant for analyzing non-Euclidean data such as probability distributions and covariance matrices.…
We build a valid p-value based on a concentration inequality for bounded random variables introduced by Pelekis, Ramon and Wang. The motivation behind this work is the calibration of predictive algorithms in a distribution-free setting. The…
Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…
This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on…
In this short note we provide an analytical formula for the conditional covariance matrices of the elliptically distributed random vectors, when the conditioning is based on the values of any linear combination of the marginal random…
We prove a Borel version of the local lemma, i.e. we show that, under suitable assumptions, if the set of variables in the local lemma has a structure of a Borel space, then there exists a satisfying assignment which is a Borel function.…