Related papers: A note on Talagrand's concentration inequality for…
We present an elementary proof for an approximate expression of the Bergman kernel on homogeneous spaces, and products of them. The error term is exponentially small with respect to the inverse semiclassical parameter.
We prove that the parabolic Harnack inequality implies the existence of jump kernel for symmetric pure jump process. This allows us to remove a technical assumption on the jumping measure in the recent characterization of the parabolic…
For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…
We prove convergence to equilibrium for a class of coagulation-fragmentation equations that do not satisfy a detailed balance condition. More precisely, we consider perturbations of constant rate kernels. Our result provides in particular…
Expectation thresholds arise from a class of integer linear programs (LPs) that are fundamental to the study of thresholds in large random systems. An avenue towards estimating expectation thresholds comes from the fractional relaxation of…
We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered…
In this article we obtain concentration inequalities for Poisson $U$-statistics $F_m(f,\eta)$ of order $m\ge 1$ with kernels $f$ under general assumptions on $f$ and the intensity measure $\gamma \Lambda$ of underlying Poisson point process…
Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…
Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an…
In this article we derive Talagrand's $T_2$ inequality on the path space w.r.t. the maximum norm for various stochastic processes, including solutions of one-dimensional stochastic differential equations with measurable drifts, backward…
We give a simple proof of Bell's inequality in quantum mechanics which, in conjunction with experiments, demonstrates that the local hidden variables assumption is false. The proof sheds light on relationships between the notion of causal…
We propose a new perspective for the evaluation of matching procedures by considering the complexity of the function class they belong to. Under this perspective we provide theoretical guarantees on post-matching covariate balance through a…
The benchmark for computation is typically given as Turing computability; the ability for a computation to be performed by a Turing Machine. Many languages exploit (indirect) encodings of Turing Machines to demonstrate their ability to…
We derive an upper bound for the mean of the supremum of the empirical process indexed by a class of functions that are known to have variance bounded by a small constant $\delta$. The bound is expressed in the uniform entropy integral of…
The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $\alpha\in(0,2]$. This process has an infinitesimal generator…
We address a special case of a conjecture of M. Talagrand relating two notions of "threshold" for an increasing family $\mathcal F$ of subsets of a finite set $V$. The full conjecture implies equivalence of the "Fractional…
Choosing models from a hypothesis space is a frequent task in approximation theory and inverse problems. Cross-validation is a classical tool in the learner's repertoire to compare the goodness of fit for different reconstruction models.…
The popular LSPE($\lambda$) algorithm for policy evaluation is revisited to derive a concentration bound that gives high probability performance guarantees from some time on.
In this paper we study the regularity of paths in terms of properties of admissible nets. We show the right concentration inequality above the modulus of continuity. Using the approach we prove the Bernstein type inequality for the…
We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these…