Related papers: A strong invariance principle for associated rando…

We prove the Almost Sure Invariance Principle (ASIP) with close to optimal error rates for nonuniformly hyperbolic maps. We do not assume exponential contraction along stable leaves, therefore our result covers in particular slowly mixing…

We present a complete characterization of the asymptotic behaviour of a correlated Bernoulli sequence { which depends on the parameter $\theta \in [0,1]$. A martingale theory based approach will allow} us to prove versions of the law of…

This article generalises the concept of realised covariation to Hilbert-space-valued stochastic processes. More precisely, based on high-frequency functional data, we construct an estimator of the trace-class operator-valued integrated…

In this paper, we investigate the law of large numbers for strictly stationary random fields, that is, we provide sufficient conditions on the moments and the dependence of the random field in order to guarantee the almost sure convergence…

The un-reduction procedure introduced previously in the context of Mechanics is extended to covariant Field Theory. The new covariant un-reduction procedure is applied to the problem of shape matching of images which depend on more than one…

Using Bernstein polynomial approximations, we prove the central limit theorem for linear spectral statistics of sample covariance matrices, indexed by a set of functions with continuous fourth order derivatives on an open interval including…

A generalization of Gy's theory for the variance of the fundamental sampling error is reviewed. Practical situations where the generalized model potentially leads to more accurate variance estimates are identified as: clustering of…

We will demonstrate that the generalized uncertainty principle exists because of the derivative expansion in the effective field theories. This is because, in the framework of the effective field theories, the minimum measurable length…

Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…

A recently proposed covariant chiral effective field theory approach is applied to study strangeness $S=-1$ hyperon-nucleon interactions at leading order. 12 low energy constants are introduced by Lorentz invariance, which is different from…

Following an early observation of Ignatowsky, we present a derivation of the transformation rules between inertial systems making no other assumptions than the existence of the latter, and show that generically these rules are characterized…

We extend, in the free probability framework, an invariance principle for multilinear homogeneous sums with low influences recently established in [E. Mossel, R. O'Donnell and K. Oleszkiewicz (2010). Noise stability of functions with low…

We prove a multivariate central limit theorem for the numbers of critical points above a level with all possible indexes of a non-necessarily isotropic Gaussian random field. In particular, we discuss the non-degeneracy of the limit…

We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly…

We provide a simple new argument for a lower bound on the coupling of a $U(1)$ gauge interaction in an effective field theory (EFT), originally obtained from the Weak Gravity Conjecture. Our argument employs basic principles of quantum…

In 2019 Anthony Quas, Philippe Thieullen and Mohamed Zarrabi introduced the concept of strong fast invertibility for linear cocycles. It relates the growth of volumes between different initial times and, together with a condition on…

This paper surveys Abelian and Tauberian theorems for long-range dependent random fields. We describe a framework for asymptotic behaviour of covariance functions or variances of averaged functionals of random fields at infinity and…

In this paper we propose an alternative to the coupling of Berkes, Liu and Wu [1] to obtain strong approximations for partial sums of dependent sequences. The main tool is a new Rosen-thal type inequality expressed in terms of the coupling…

In this paper we deal with a large class of dynamical systems having a version of the spectral gap property. Our primary class of systems comes from random dynamics, but we also deal with the deterministic case. We show that if a random…

This note investigates invariance principles for sums of N(nt) iid radom variables, where n is an integer, t is a positive real number and N(u) is a stochastic process with nonnegative integer values. We show that the sequence of sums of…