Related papers: Stability and approximation of statistical limit l…

In this paper, we prove that, under precise spectral assumptions, some finite difference approximations of scalar leftgoing transport equations on the positive half-line with numerical boundary conditions are $\ell^1$-stable but…

We prove a convergence theorem for U-statistics of degree two, where the data dimension $d$ is allowed to scale with sample size $n$. We find that the limiting distribution of a U-statistic undergoes a phase transition from the…

We complete a full classification of non-degenerate traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under (piecewise) smooth perturbations. A striking feature of our analysis is…

This paper deals with the large deviations behavior of a stochastic process called thinned Levy process. This process appeared recently as a stochastic-process limit in the context of critical inhomogeneous random graphs. The process has a…

In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…

We study chaotic orbits of conservative low--dimensional maps and present numerical results showing that the probability density functions (pdfs) of the sum of $N$ iterates in the large $N$ limit exhibit very interesting time-evolving…

Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a…

We prove stochastic stability of absolutely continuous invariant measures (ACIMs) for piecewise expanding $C^{1+\varepsilon}$ maps of the interval. For maps $\tau$ in the class $\mathcal{T}([0,1]; s, \varepsilon)$, we consider perturbed…

We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke)…

The stationary distribution of a fully chaotic system typically exhibits a fractal structure, which dramatically changes if the dynamical equations are even slightly modified. Perturbative techniques are not expected to work in this…

In this paper we show that the limiting distribution of the real and the imaginary part of the double Fourier transform of a stationary random field is almost surely an independent vector with Gaussian marginal distributions, whose variance…

We establish self-norming central limit theorems for non-stationary time series arising as observations on sequential maps possessing an indifferent fixed point. These transformations are obtained by perturbing the slope in the…

Some scales of spaces of ultra-differentiable functions are introduced, having good stability properties with respect to infinitely many derivatives and compositions. They are well-suited for solving non-linear functional equations by means…

In statistical mechanics, evaluating finite-size macroscopic fluctuations typically relies on Edgeworth expansions. However, these perturbative methods append additive polynomial corrections that inevitably break down in the large deviation…

We consider the globally modified stochastic (hyperviscous) Navier-Stokes equations with transport noise on 3D torus. We first establish the existence and pathwise uniqueness of the weak solutions, and then show their convergence to the…

This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. We do not require the components to be identically…

For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…

We consider the incompressible 2D Navier-Stokes equations with periodic boundary conditions driven by a deterministic time periodic forcing and a degenerate stochastic forcing. We show that the system possesses a unique ergodic periodic…

We study the asymptotic distributions of the spiked eigenvalues and the largest nonspiked eigenvalue of the sample covariance matrix under a general covariance matrix model with divergent spiked eigenvalues, while the other eigenvalues are…

For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n}…