相关论文: A Study Of Some Generalized Central Sets Theorem A…

A theorem of L. Caffarelli implies the existence of a map pushing forward a source Gaussian measure to a target measure which is more log-concave than the source one, which contracts Euclidean distance (in fact, Caffarelli showed that the…

A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…

We give a new proof of the classical Central Limit Theorem, in the Mallows ($L^r$-Wasserstein) distance. Our proof is elementary in the sense that it does not require complex analysis, but rather makes use of a simple subadditive inequality…

We prove that the central sequence algebra of a separable C*-algebra is either subhomogeneous or non-exact, confirming a conjecture of Enders and Shulman. We also prove analogous dichotomy for other massive C*-algebras.

Green, Tao and Ziegler prove ``Dense Model Theorems'' of the following form: if R is a (possibly very sparse) pseudorandom subset of set X, and D is a dense subset of R, then D may be modeled by a set M whose density inside X is…

One of the two basic theorems in [5] on the existence of solutions of PDEs is improved with the use of a group analysis type argument.

A nonlinear generalization of convergence sets of formal power series, in the sense of Abhyankar-Moh, is introduced. Given a family y=\phi_{s}(t,x)=sb_{1}(x)t+b_{2}(x)t^{2}+... of analytic curves in C\timesC^{n} passing through the origin,…

We derive a central limit theorem for sums of a function of independent sums of independent and identically distributed random variables. In particular we show that previously known result from Rempa\la and Weso\lowski (Statist. Probab.…

We check claims for a generalized central limit theorem holding at the Feigenbaum (infinite bifurcation) point of the logistic map, made recently by U. Tirnakli, C. Beck, and C. Tsallis (Phys. Rev. {\bf 75}, 040106(R) (2007)). We show that…

A central limit theorem for the integrated squared error of the directional-linear kernel density estimator is established. The result enables the construction and analysis of two testing procedures based on squared loss: a nonparametric…

In this paper, we prove that the "conformal collider bounds" originally proposed by Hofman and Maldacena hold for any unitary parity-preserving conformal field theory (CFT) with a unique stress tensor in spacetime dimensions larger than 2.…

We prove the conjectured limiting normality for the number of crossings of a uniformly chosen set partition of [n] = {1,2,...,n}. The arguments use a novel stochastic representation and are also used to prove central limit theorems for the…

In Dolera, Gabetta and Regazzini [Ann. Appl. Probab. 19 (2009) 186-201] it is proved that the total variation distance between the solution $f(\cdot,t)$ of Kac's equation and the Gaussian density $(0,\sigma^2)$ has an upper bound which goes…

By classical results of G.C. Evans and G. Choquet on "good kernels $G$ in potential theory", for every polar $K_\sigma$-set $P$, there exists a finite measure $\mu$ on $P$ such that $G\mu=\infty$ on $P$, and a set $P$ admits a finite…

We derive a strong law of large numbers, a central limit theorem, a law of the iterated logarithm and a large deviation theorem for so-called deviation means of independent and identically distributed random variables (for the strong law of…

Nourdin et al. [9] established the following universality result: if a sequence of off-diagonal homogeneous polynomial forms in i.i.d. standard normal random variables converges in distribution to a normal, then the convergence also holds…

For more than a century, Cantor's theory of transfinite numbers has played a pivotal role in set theory, with ramifications that extend to many areas of mathematics. This article extends earlier findings with a fresh look at the critical…

The classical H. Poincar\'{e} Center-Focus problem asks about the characterization of planar polynomial vector fields such that all their integral trajectories are closed curves whose interiors contain a fixed point, a {\em center}. This…

We prove a fixed point theorem for closed-graphed, decomposable-valued correspondences whose domain and range is a decomposable set of functions from an atomless measure space to a topological space. One consequence is an improvement of the…

In classical estimation theory, the central limit theorem implies that the statistical error in a measurement outcome can be reduced by an amount proportional to n^(-1/2) by repeating the measures n times and then averaging. Using quantum…