Related papers: On a Berry-Esseen type limit theorem for Boolean c…

For the stochastic six-vertex model on the quadrant $\mathbb{Z}_{\geq0}\times\mathbb{Z}_{\geq0}$ with step initial conditions and a single second-class particle at the origin, we show almost sure convergence of the speed of the second-class…

In this paper, we consider the explicit bound for the second-order approximation of the quadratic variation of a general fractional Gaussian process $(G_t)_{t\ge 0}$. The second order mixed partial derivative of the covariance function $…

We give optimal convergence rates in the central limit theorem for a large class of martingale difference sequences with bounded third moments. The rates depend on the behaviour of the conditional variances and for stationary sequences the…

It is known that the number of points in the largest cluster of a percolating Poisson process restricted to a large finite box is asymptotically normal. In this note, we establish a rate of convergence for the statement. As each point in…

We establish a general Berry-Esseen type bound which gives optimal bounds in many situations under suitable moment assumptions. By combining the general bound with Palm theory, we deduce a new error bound for assessing the accuracy of…

Let $A_n= \varepsilon_n \cdots \varepsilon_1$, where $(\varepsilon_n)_{n \geq 1}$ is a sequence of independent random matrices taking values in $ GL_d(\mathbb R)$, $d \geq 2$, with common distribution $\mu$. In this paper, under standard…

Let $Q$ be a transition probability on a measurable space $E$ which admits an invariant probability measure, let $(X_n)_n$ be a Markov chain associated to $Q$, and let $\xi$ be a real-valued measurable function on $E$, and $S_n=\sum…

We will prove the Berry-Esseen theorem for the number counting function of the circular $\beta$-ensemble (C$\beta$E), which will imply the central limit theorem for the number of points in arcs of the unit circle in mesoscopic and…

The number of faces of the convex hull of $n$ independent and identically distributed random points chosen on the boundary of a smooth convex body in $\mathbb{R}^d$ is investigated. In dimensions two and three the number of $k$-faces is…

We investigate the rate of convergence in the central limit theorem for convex sets. We obtain bounds with a power-law dependence on the dimension. These bounds are asymptotically better than the logarithmic estimates which follow from the…

Quantum speed limit is a fundamental speed limit for the evolution of quantum states. It is the single-most important interpretation of the time energy uncertainty relation. Recently the speed limit of quantum correlations have been…

We obtain the uniform convergence rate for the Gaussian fluctuation of the radial part of the Brownian motion on a hyperbolic space. We also show that this result is sharp if the dimension of the hyperbolic space is two or general odd. Our…

Quantum speed limit is bound on the minimum time a quantum system requires to evolve from an initial state to final state under a given dynamical process. It sheds light on how fast a desired state transformation can take place which is…

We consider a slow-fast stochastic differential system with L\'evy noise. We will employ the perturbed test function method to study the normal deviation of the slow-fast system. Our main result states that the deviation can be approximated…

We prove central limit theorems for the number of descents and the number of inversions after a shelf-shuffle. In particular, we bound the convergence rate for the number of inversions independently of the number of shelves. Along the way,…

We obtain almost optimal convergence rate in the central limit theorem for "nonconevntional" sums of the form $S_N=N^{-\frac12}\sum_{n=1}^N (F(\xi_n,\xi_{2n},...,\xi_{\ell n})-\bar F)$.

Stein's method allows to prove distributional convergence of a sequence of random variables and to quantify it with respect to a given metric such as Kolmogorov's (a Berry-Ess\'een type theorem). Mod-* convergence quantifies the convergence…

We construct inner products by the Bernstein-Markov inequality on spaces of holomorphic sections of high powers of a line bundle. The corresponding weighted Bergman kernel functions converge to an extremal function. We obtain a uniform…

Central limit theorems (CLTs) for high-dimensional random vectors with dimension possibly growing with the sample size have received a lot of attention in the recent times. Chernozhukov et al. (2017) proved a Berry--Esseen type result for…

The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…