Related papers: Generalized Hermite processes, discrete chaos and …
We analyze {\em the Rosenblatt process} which is a selfsimilar process with stationary increments and which appears as limit in the so-called {\em Non Central Limit Theorem} (Dobrushin and Major (1979), Taqqu (1979)). This process is…
Non-stationary version of unitary quantum mechanics formulated in non-Hermitian (or, more precisely, in hiddenly Hermitian) interaction-picture representation is illustrated via an elementary $N$ by $N$ matrix Hamiltonian $H(t)$ mimicking a…
In the averaging process on a graph $G = (V, E)$, a random mass distribution $\eta$ on $V$ is repeatedly updated via transformations of the form $\eta_{v}, \eta_{w} \mapsto (\eta_{v} + \eta_{w})/2$, with updates made according to…
In this article, we consider limit theorems for some weighted type random sums (or discrete rough integrals). We introduce a general transfer principle from limit theorems for unweighted sums to limit theorems for weighted sums via rough…
A family of log-correlated Gaussian processes indexed by metric spaces is introduced, when the metric is conditionally negative definite. These processes arise as the limit of bi-fractional Brownian motions indexed by $(H,K)$ scaled by…
We compute the joint distribution of singular numbers for all principal corners of a $p$-adic Hermitian (resp. alternating) matrix with additive Haar distribution, the non-archimedean analogue of the GUE (resp. aGUE) corners process. In the…
We study weighted sum processes associated to elements in a Wiener chaos with fixed order. More precisely, we show H\"older estimates and a functional limit theorem for them. Main tools we use are the integration by parts formula in…
Consider $Z^f_t(u)=\int_0^{tu}f(N_s) ds$, $t>0$, $u\in[0,1]$, where $N=(N_t)_{t\in\mathbb{R}}$ is a normal process and $f$ is a measurable real-valued function satisfying $Ef(N_0)^2<\infty$ and $Ef(N_0)=0$. If the dependence is sufficiently…
Generalized linear (GL-) statistics are defined as functionals of an U-quantile process and unify different classes of statistics such as U-statistics and L-statistics. We derive a central limit theorem for GL-statistics of strongly mixing…
We classify all subsets $S$ of the projective Hilbert space with the following property: for every point $\pm s_0\in S$, the spherical projection of $S\backslash\{\pm s_0\}$ to the hyperplane orthogonal to $\pm s_0$ is isometric to…
We prove that a normalized sequence of multiple Wigner integrals (in a fixed order of free Wigner chaos) converges in law to the standard semicircular distribution if and only if the corresponding sequence of fourth moments converges to 2,…
We present a procedure for averaging one-parameter random unitary groups and random self-adjoint groups. Central to this is a generalization of the notion of weak convergence of a sequence of measures and the corresponding generalization of…
Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point…
Using normalized Hermite functions, we construct bases in the space of square integrable functions on the unit circle ($L^2(\mathcal C)$) and in $l_2(\mathbb Z)$, which are related to each other by means of the Fourier transform and the…
In the present paper, fixed trace $\beta$-Hermite ensembles generalizing the fixed trace Gaussian Hermite ensemble are considered. For all $\beta$, we prove the Wigner semicircle law for these ensembles by using two different methods: one…
We study certain linear and antilinear symmetry generators and involution operators associated with pseudo-Hermitian Hamiltonians and show that the theory of pseudo-Hermitian operators provides a simple explanation for the recent results of…
We present two limit theorems, a mean ergodic and a central limit theorem, for a specific class of one-dimensional diffusion processes that depend on a small-scale parameter $\varepsilon$ and converge weakly to a homogenized diffusion…
For general thinning procedures, its inverse operation, the condensing, is studied and a link to integration-by-parts formulas is established. This extends the recent results on that link for independent thinnings of point processes to…
We provide a particle picture representation for the non-symmetric Rosenblatt process and for Hermite processes of any order, extending the result of Bojdecki, Gorostiza and Talarczyk in~\cite{FILT}. We show that these processes can be…
We prove functional central and non-central limit theorems for generalized variations of the anisotropic $d$-parameter fractional Brownian sheet (fBs) for any natural number $d$. Whether the central or the non-central limit theorem applies…