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Giuseppe Lamberti

Publications and source records attributed to Giuseppe Lamberti.

7 recordsLinked to original sources
arXiv2026

Discrete random Clark measures and associated inner functions

We study a class of random inner functions $\varphi$ whose Clark measure at $1$ is the weighted sum of point masses supported on independent uniformly distributed points of $\mathbb T$. Our first result shows that $\varphi$ is almost surely a Blaschke product. We then investigate when $\varphi$ admits angular derivative almost surely and we provide a $0 - 1$ law. These conditions have a direct interpretation in terms of the other Clark measures associated with $\varphi$. Finally, we obtain quantitative estimates for the zeros of $\varphi$, proving that, in suitable regimes, their distribution satisfies summability conditions stronger than the classical Blaschke condition.

math.CV↗
arXiv2026

Separation properties of a hybrid point process with determinantal radii and uniform arguments

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 required to characterize the separated Poisson processes with the same first intensities as $\Lambda_\phi$. To gain further insight into this different behavior, we center our attention to radial weights $\phi(z)$ and introduce a hybrid process $\Lambda_\phi^M=\{r_k e^{i\theta_k}\}_{k=1}^\infty$, where the moduli $r_k$ are taken from $\Lambda_\phi$, while the arguments $\theta_k$ are chosen independently and uniformly in $[0,2\pi)$. Our main result is that $\Lambda_\phi^M$ is almost surely separated if and only if its first intensity satisfies the same condition as in the Poisson case.

math.CV↗
arXiv2025

Interpolation and random interpolation in de Branges-Rovnyak spaces

The aim of this paper is to characterize universal and multiplier interpolating sequences for de Branges-Rovnyak spaces H (b) where the defining function b is a general non-extreme rational function. Our results carry over to recently introduced higher order local Dirichlet spaces and thus generalize previously known results in classical local Dirichlet spaces. In this setting, we also investigate random interpolating sequences with prescribed radii, providing a 0 -1 law. This condition is automatic when b is rational non inner so that we can assume H (b) = M(a). By standard results in functional analysis, the corresponding norms are equivalent. In [18], the authors demonstrated that the decomposition (1) is orthogonal in the metric of M(a).

math.CV↗
arXiv2025

Separated determinantal point processes and generalized Fock spaces

We study conditions so that the determinantal point process $\Lambda_\phi$ associated to a generalized Fock space defined by a doubling subharmonic weight $\phi$ is almost surely a separated sequence in $\mathbb C$. Under a natural assumption on $\phi$, we provide a characterization of such processes. Additionally, we emphasize the role of intrinsic repulsion in determinantal processes by comparing $\Lambda_\phi$ with the Poisson process of the same first intensity. As an application, we show that the determinantal process $\Lambda_\alpha$ associated to the canonical weight $\phi_\alpha(z)=|z|^\alpha$, $\alpha>0$, is almost surely separated if and only if $\alpha<4/3$. In contrast, the Poisson process $\Lambda_\alpha^P$ having the same first intensity as $\Lambda_\alpha$ is almost surely separated if and only if $\alpha<1$.

math.CV↗
arXiv2024

Random interpolation in the Nevanlinna and Smirnov classes and related spaces

We study random interpolating sequences with prescribed radii in the Nevanlinna and Smirnov classes. As it turns out these are characterized by the Blaschke condition. This follows from a more general result. Indeed, we show that this characterization is true in so-called big Hardy-Orlicz spaces. It is noteworthy to mention that conditions for deterministic interpolation in these spaces are given by harmonic majorants, the existence of which is difficult to check in general.

math.CV↗
arXiv2024

Random Carleson Sequences for the Hardy space on the Polydisc and the Unit Ball

We study the Kolmogorov 0-1 law for a random sequence with prescribed radii so that it generates a Carleson measure almost surely, both for the Hardy space on the polydisc and the Hardy space on the unit ball, thus providing improved versions of previous results of the first two authors and of a separate result of Massaneda. In the polydisc, the geometry of such sequences is not well understood, so we proceed by studying the random Gramians generated by random sequences, using tools from the theory of random matrices. Another result we prove, and that is of its own relevance, is the 0-1 law for a random sequence to be partitioned into M separated sequences with respect to the pseudo-hyperbolic distance, which is used also to describe the random sequences that are interpolating for the Bloch space on the unit disc almost surely.

math.CV↗