Related papers: A concentration inequality for interval maps with …
We consider Lipschitz maps with values in quasi-metric spaces and extend such maps to finitely many points. We prove that in this context every 1-Lipschitz map admits an extension such that its Lipschitz constant is bounded from above by…
In the present paper we prove several results concerning the existence of low-discrepancy point sets with respect to an arbitrary non-uniform measure $\mu$ on the $d$-dimensional unit cube. We improve a theorem of Beck, by showing that for…
We obtain bounds on fluctuations of two entropy estimators for a class of one-dimensional Gibbs measures on the full shift. They are the consequence of a general exponential inequality for Lipschitz functions of n variables. The first…
We study the Wasserstein distance of order 1 between the empirical distribution and the marginal distribution of stationary $\alpha$-dependent sequences. We prove some moments inequalities of order p for any p $\ge$ 1, and we give some…
The property of measure concentration is that an arbitrary 1-Lipschitz function $f:X\to \mathbb{R}$ on an mm-space $X$ is almost close to a constant function. In this paper, we prove that if such a concentration phenomenon arise, then any…
We provide a sharp rate of convergence in the central limit theorem for random vectors with an unconditional, log-concave density. The argument relies on analysis of the Neumann laplacian on convex domains and on the theory of optimal…
It is well known that the Liverani-Saussol-Vaienti map satisfies a central limit theorem for H\"older observables in the parameter regime where the correlations are summable. We show that when $C^2$ observables are considered, the variance…
We study decaying half-line Schr\"odinger operators and the local eigenvalue spacing of their Dirichlet restrictions. While absolutely continuous spectrum is strongly associated with bulk universality and clock behavior, singular spectral…
Barcodes form a complete set of invariants for interval decomposable persistence modules and are an important summary in topological data analysis. The set of barcodes is equipped with a canonical one-parameter family of metrics, the…
Let L be an ample holomorphic line bundle over a compact complex Hermitian manifold X. Any fixed smooth Hermitian metric on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k:th tensor power…
This paper is devoted to the problem of determining the concentration bounds that are achievable in non-parametric regression. We consider the setting where features are supported on a bounded subset of $\mathbb{R}^d$, the regression…
A crucial assumption in most statistical learning theory is that samples are independently and identically distributed (i.i.d.). However, for many real applications, the i.i.d. assumption does not hold. We consider learning problems in…
We obtain rates of convergence in the weak invariance principle (functional central limit theorem) for $\R^d$-valued H\"older observables of nonuniformly hyperbolic maps. In particular, for maps modelled by a Young tower with…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
A cornerstone of special relativity is Lorentz Invariance, the postulate that all observers measure exactly the same photon speeds independently on the photon energies. However, a hypothesized structure of spacetime may alter this…
We consider intermittent maps T of the interval, with an absolutely continuous invariant probability measure \mu. Kim showed that there exists a sequence of intervals A_n such that \sum \mu(A_n)=\infty, but \{A_n\} does not satisfy the…
We study concentration inequalities for the Kullback--Leibler (KL) divergence between the empirical distribution and the true distribution. Applying a recursion technique, we improve over the method of types bound uniformly in all regimes…
We give bounds on the Poincare (inverse spectral gap) constant of a non-negative, integer-valued random variable W, under negative dependence assumptions such as ultra log-concavity and total negative dependence. We show that the bounds…
We show that confidence intervals in a variance component model, with asymptotically correct uniform coverage probability, can be obtained by inverting certain test-statistics based on the score for the restricted likelihood. The results…
A sharp, distribution free, non-asymptotic result is proved for the concentration of a random function around the mean function, when the randomization is generated by a finite sequence of independent data and the random functions satisfy…