Related papers: Type B Gaussian Statistics as Noncommutative Centr…
Bessel processes $(X_{t,k})_{t\ge0}$ in $N$ dimensions are classified via associated root systems and multiplicity constants $k\ge0$. They describe interacting Calogero-Moser-Suther\-land particle systems with $N$ particles and are related…
Let $T$ be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry--Esseen type bounds for $T$ are obtained. The bounds are the best possible for many known statistics.…
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…
The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…
We give an overview of the recent asymptotic results on the geometry of excursion sets of stationary random fields. Namely, we cover a number of limit theorems of central type for the volume of excursions of stationary (quasi--, positively…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
Applying an inductive technique for Stein and zero bias couplings yields Berry-Esseen theorems for normal approximation for two new examples. The conditions of the main results do not require that the couplings be bounded. Our two…
Selecting between different dependency structures of hidden Markov random field can be very challenging, due to the intractable normalizing constant in the likelihood. We answer this question with approximate Bayesian computation (ABC)…
We show that the centered maximum of a sequence of log-correlated Gaussian fields in any dimension converges in distribution, under the assumption that the covariances of the fields converge in a suitable sense. We identify the limit as a…
We consider gauged sigma-models from a Riemann surface into a Kaehler and hamiltonian G-manifold X. The supersymmetric N=2 theory can always be twisted to produce a gauged A-model. This model localizes to the moduli space of solutions of…
We show that the three-point skewness of concentration fluctuations is non-vanishing in free liquid diffusion, even in the limit of vanishingly small mean concentration gradients. We exploit a high-Schmidt reduction of nonlinear…
We give sufficient conditions on the exponent $p: \mathbb R^d\rightarrow [1,\infty)$ for the boundedness of the non-centered Gaussian maximal function on variable Lebesgue spaces $L^{p(\cdot)}(\mathbb R^d, \gamma_d)$, as well as of the new…
This work introduces a new, explicit bound on the Hellinger distance between a continuous random variable and a Gaussian with matching mean and variance. As example applications, we derive a quantitative Hellinger central limit theorem and…
We study the joint distribution of descents and sign for elements of the symmetric group and the hyperoctahedral group (Coxeter groups of types $A$ and $B$). For both groups, this has an application to riffle shuffling: for large decks of…
Mesoscopic interacting Bose-Einstein condensates confined in a few traps display phase transitions that cannot be explained with a mean field theory. By describing each trap as an effective site of a Bose-Hubbard model and using the…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
Our purpose is to prove central limit theorem for countable nonhomogeneous Markov chain under the condition of uniform convergence of transition probability matrices for countable nonhomogeneous Markov chain in Ces\`aro sense. Furthermore,…
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…
Using recently proposed non-linearly realized supersymmetry in non-Abelian gauge theory corrected to the order (alpha')^2, we derive the non-linear BPS equations in the background B-field for the U(2) monopoles and instantons. We show that…
Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…