Related papers: Inhomogeneous Poisson processes in the disk and in…

We study conditional independence under infinite measures on punctured product spaces, a notion recently introduced for graphical modeling in multivariate extremes and L\'evy processes. In contrast to classical probabilistic conditional…

Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_0$ and intensity $\lambda_0$. We take a nonparametric Bayesian approach to the…

We recently characterized the separated determinantal point processes $\Lambda_\phi$ associated with Fock spaces $\mathcal F_\phi$ in the plane with doubling weight $\phi$. We also showed that, as expected, a more restrictive condition is…

We completely characterize those positive Borel measures $\mu$ on the unit ball $\mathbb{B}_ n$ such that the Carleson embedding from Hardy spaces $H^p$ into the tent-type spaces $T^q_ s(\mu)$ is bounded, for all possible values of…

In this paper we study the properties of the Poisson random measure and the Poisson integral associated with a G-Levy process. We prove that a Poisson integral is a G-Levy process and give the conditions which ensure that a Poisson integral…

Let $0<p<\infty$ and $\Psi: [0,1) \to (0,\infty)$, and let $\mu$ be a finite positive Borel measure on the unit disc $\mathbb{D}$ of the complex plane. We define the Lebesgue-Zygmund space $L^p_{\mu,\Psi}$ as the space of all measurable…

We study the invariant subspaces generated by inner functions for a class of $\mathcal{P}^t(\mu)$-spaces which can be identified as spaces of analytic functions in the unit disk $\mathbb{D}$, where $\mu$ is a measure supported in the closed…

This article investigates the phenomenon of maximal rigidity in spatial processes, where perfect interpolation of the process is possible from partial information, specifically, from its restriction to a strict subdomain, often resulting in…

We study locally compact metric spaces that enjoy various forms of homogeneity with respect to M\"obius self-homeomorphisms. We investigate connections between such homogeneity and the combination of isometric homogeneity with…

We consider the random interlacements process with intensity $u$ on ${\mathbb Z}^d$, $d\ge 5$ (call it $I^u$), built from a Poisson point process on the space of doubly infinite nearest neighbor trajectories on ${\mathbb Z}^d$. For $k\ge 3$…

This paper extends the known characterization of interpolation and sampling sequences for Bergman spaces to the mixed-norm spaces. The Bergman spaces have conformal invariance properties not shared by the mixed-norm spaces. As a result,…

Poisson processes in the space of $k$-dimensional totally geodesic subspaces ($k$-flats) in a $d$-dimensional standard space of constant curvature $\kappa\in\{-1,0,1\}$ are studied, whose distributions are invariant under the isometries of…

In this paper, we study invariant Poisson processes of lines (i.e, bi-infinite geodesics) in the $3$-regular tree. More precisely, there exists a unique (up to multiplicative constant) locally finite Borel measure on the space of lines that…

In this paper we study nonlinear interpolation problems for interpolation and peak-interpolation sets of function algebras. The subject goes back to the classical Rudin-Carleson interpolation theorem. In particular, we prove the following…

We study the mutual regularity properties of Palm measures of point processes, and establish that a key determining factor for these properties is the rigidity-tolerance behaviour of the point process in question (for those processes that…

In this paper, we study the Poisson problem involving a fractional Hardy operator and a measure source. The complex interplay between the nonlocal nature of the operator, the peculiar effect of the singular potential and the measure source…

Let $\mu_{g}$ and $\mu_{p}$ denote the Gaussian and Poisson measures on ${\Bbb R}$, respectively. We show that there exists a unique measure $\widetilde{\mu}_{g}$ on ${\Bbb C}$ such that under the Segal-Bargmann transform $S_{\mu_g}$ the…

We provide some new sharp embeddings for p-Carleson and related measures in the unit disk of the complex plane

We calculate, in a relatively explicit way, the Hamiltonian systems which arise from the Evens-Lu construction of homogeneous Poisson structures on both compact and noncompact type symmetric spaces. A corollary is that the Hamiltonian…

We focus on the estimation of the intensity of a Poisson process in the presence of a uniform noise. We propose a kernel-based procedure fully calibrated in theory and practice. We show that our adaptive estimator is optimal from the oracle…