Related papers: Point processes and the infinite symmetric group. …
Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter $\theta$ approaches infinity. The motivation for these results is to understand the…
We investigate a family of discrete-time stationary processes defined by multiple stable integrals and renewal processes with infinite means. The model may exhibit behaviors of short-range or long-range dependence, respectively, depending…
The two-parameter Poisson--Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
We report some properties of heavy-tailed Sibuya-like distributions related to thinning, self-decomposability and branching processes. Extension of the thinning operation of on-negative integer-valued random variables to scaling by…
We present a technique to study normalizing strategies when termination is asymptotic, that is, it appears as a limit, as opposite to reaching a normal form in a finite number of steps. Asymptotic termination occurs in several settings,…
Determinantal point processes are characterized by a special structural property of the correlation functions: they are given by minors of a correlation kernel. However, unlike the correlation functions themselves, this kernel is not…
This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing…
We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set…
This work concerns the dynamical two-point spin correlation functions of the transverse Ising quantum chain at finite (non-zero) temperature, in the universal region near the quantum critical point. They are correlation functions of twist…
We consider the FCFS G/G/n queue in the Halfin-Whitt regime, in the presence of heavy-tailed distributions (i.e. infinite variance). We prove that under minimal assumptions, i.e. only that processing times have finite 1 + epsilon moment and…
In this paper, we establish the precise asymptotic behaviors of the tail probability and the transition density of a large class of isotropic L\'evy processes when the scaling order is between 0 and 2 including 2. We also obtain the precise…
This paper is devoted to the analysis of the finite-dimensional distributions and asymptotic behavior of extremal Markov processes connected to the Kendall convolution. In particular, based on its stochastic representation, we provide…
We derive the asymptotic behaviour of the genealogy of a logistic branching process in the setting where the equilibrium population size is large. In three regimes on the tail of the offspring distribution we recover the Kingman,…
The infinitesimal transition probability operator for a continuous-time discrete-state Markov process, $\mathcal{Q}$, can be decomposed into a symmetric and a skew-symmetric parts. As recently shown for the case of diffusion processes,…
The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution…
The areas under workload process and under queuing process in a single server queue over the busy period have many applications not only in queuing theory but also in risk theory or percolation theory. We focus here on the tail behaviour of…
We consider a symmetric exclusion process on a discrete interval of $S$ points with various boundary conditions at the endpoints. We study the asymptotic decay of correlations as $S\to\infty$. The main result is asymptotic independence of a…
It is shown that for a non-decreasing self-similar stochastic process $T$ with independent increments, the range of $T$ forms a Poisson point process with $\sigma$-finite intensity if and only if the one-dimensional distribution of $T(1)$…
$L$-ensembles are a class of determinantal point processes which can be viewed as a statistical mechanical systems in the grand canonical ensemble. Circulant $L$-ensembles are the subclass which are locally translationally invariant and…