相关论文: Noncentral limit results for spatiotemporal random…
We extend the spectral method for proving limit theorems to random non-uniformly expanding dynamical systems. This yields the CLT and moderate deviations principles (MDP). We show that as the amount of non-uniformity decreases the CLT rates…
Consider a $N\times n$ random matrix $Y_n=(Y_{ij}^{n})$ where the entries are given by $$ Y_{ij}^{n}=\frac{\sigma_{ij}(n)}{\sqrt{n}} X_{ij}^{n} $$ the $X_{ij}^{n}$ being centered, independent and identically distributed random variables…
Random hyperspherical harmonics are Gaussian Laplace eigenfunctions on the unit $d$-dimensional sphere ($d\ge 2$). We study the convergence in Total Variation distance for their nonlinear statistics in the high energy limit, i.e., for…
We establish asymptotically Gaussian fluctuations for functionals of a large class of spin models and strongly correlated random point fields, achieving near-optimal rates. For spin models, we demonstrate Gaussian asymptotics for the…
Relativistic QFTs are in general defined by a collection of effective actions, describing the dynamics of quantum fields at different energy scales. The consequent natural idea of a space of theories is still a rather imprecise notion,…
Suppose $X = (X_x, x$ in $Z^d)$ is a family of i.i.d. variables in some measurable space, $B_0$ is a bounded set in $R^d$, and for $t > 1$, $H_t$ is a measure on $tB_0$ determined by the restriction of $X$ to lattice sites in or adjacent to…
In this paper, we study fluctuations of conditionally centered statistics of the form $$N^{-1/2}\sum_{i=1}^N c_i(g(\sigma_i)-\mathbb{E}_N[g(\sigma_i)|\sigma_j,j\neq i])$$ where $(\sigma_1,\ldots ,\sigma_N)$ are sampled from a dependent…
We study the fluctuations of the eigenvalues of real valued large centrosymmetric random matrices via its linear eigenvalue statistic. This is essentially a central limit theorem (CLT) for sums of dependent random variables. The dependence…
For a sequence of immersed connected closed Hamiltonian stationary Lagrangian submaniolds in $\mathbb{C}^{n}$ with uniform bounds on their volumes and the total extrinsic curvatures, we prove that a subsequence converges either to a point…
Two central limit theorems for sample Fr\'echet means are derived, both significant for nonparametric inference on non-Euclidean spaces. The first one, Theorem 2.2, encompasses and improves upon most earlier CLTs on Fr\'echet means and…
We establish a central limit theorem (CLT) for families of products of $\epsilon$-independent random variables. We utilize graphon limits to encode the evolution of independence and characterize the limiting distribution. Our framework…
Suppose that $\{u(t\,, x)\}_{t >0, x \in\mathbb{R}^d}$ is the solution to a $d$-dimensional stochastic heat equation driven by a Gaussian noise that is white in time and has a spatially homogeneous covariance that satisfies Dalang's…
In [Kozma-Toth, Ann. Probab. v 45, pp 4307-4347 (2017)] the weak CLT was established for random walks in doubly stochastic (or, divergence-free) random environments, under the following conditions: 1. Strict ellipticity assumed for the…
Under reasonable algebraic assumptions and under an infinite second order moment assumption, we show that the logarithm of the norm (log-norm) of a product of random i.i.d. matrices with entries in $\mathbb{R}$ or in any other local field…
Interior solutions of Einstein's equations with a non-zero cosmological constant are given for static and spherically symmetric configurations of uniform density. The metric tensor and pressure are determined for both positive and negative…
We investigate the nonrelativistic quantum dynamics of a spinless particle in a screw-type spacetime endowed with two independent twist controls that interpolate between a pure screw dislocation and a homogeneous twist. From the induced…
We present a new approach, inspired by Stein's method, to prove a central limit theorem (CLT) for linear statistics of $\beta$-ensembles in the one-cut regime. Compared with the previous proofs, our result requires less regularity on the…
The notion of uniform and/or constant tensor fields of rank $>0$ is incompatible with general curved spacetimes. This work considers the consequences of certain tensor-valued coefficients for Lorentz violation in the Standard-Model…
We aim to generalize the homogenisation theorem in \cite{Gehringer-Li-tagged} for a passive tracer interacting with a fractional Gau{\ss}ian noise to also cover fractional non-Gau{\ss}ian noises. To do so we analyse limit theorems for…
We consider the FRW cosmological model in which the matter content of universe (playing a role of inflaton or quintessence) is given by a novel generalization of the massive scalar field. The latter is a scalar version of the recently…