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We present some correlated fractional counting processes on a finite time interval. This will be done by considering a slight generalization of the processes in Borges et al. (2012). The main case concerns a class of space-time fractional…
Experiments performed on quantum systems often measure multitime correlation functions. When quantum systems are weakly coupled to their environment, the time evolution of such correlation functions can be reduced to that of the reduced…
This paper studies the asymptotic distribution of a constrained lasso-type estimator for denoising signals defined on the nodes of a graph, where the underlying structure encodes relationships between variables. We show that, under suitable…
We propose a method to substantially improve the signal-to-noise ratio of lattice correlation functions for bosonic operators or other operator combinations with disconnected contributions. The technique is applicable for correlations…
Various inflationary scenarios can often be distinguished from one another by looking at the squeezed limit behavior of correlation functions. Therefore, it is useful to have a framework designed to study this limit in a more systematic and…
Filtered Poisson processes are often used as reference models for intermittent fluc- tuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical…
Brooding over bosons, wave packets and Bose - Einstein correlations, we present a generic quantum mechanical system that contains arbitrary number of bosons characterized by wave-packets and that can undergo a Bose-Einstein condensation…
We study effects of independent white noise on synchronization phenomena in ensembles of coupled limit cycle oscillators with different native frequencies. We consider a simple model where the ensemble consists of two inter-connected…
A detailed understanding of all effects and influences on higher-order correlations is essential. At low charged multiplicity, the effect of a nonpoissonian multiplicity distribution can significantly distort correlations. Evidently, the…
Through a reformulation of the local limit theorem and law of small numbers, which is obtained by working in the spaces naturally associated to the limiting distributions, we discover a general and abstract framework for the investigation…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
The theory of sparse stochastic processes offers a broad class of statistical models to study signals. In this framework, signals are represented as realizations of random processes that are solution of linear stochastic differential…
We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…
Gaussian bounds on noise correlation of functions play an important role in hardness of approximation, in quantitative social choice theory and in testing. The author (2008) obtained sharp gaussian bounds for the expected correlation of…
Starting with an operator in the universal enveloping algebra of a semi-simple, complex Lie group the nearest neighbor statistics of the spectra of this operator along a sequence of representations are discussed. After a short introduction…
In this paper we present a rigorous asymptotic analysis for stochastic systems with two fast relaxation times. The mathematical model analyzed in this paper consists of a Langevin equation for the particle motion with time-dependent force…
In this paper we derive tight bounds on the expected value of products of {\em low influence} functions defined on correlated probability spaces. The proofs are based on extending Fourier theory to an arbitrary number of correlated…
We consider the field theory of $N$ massless bosons which are free except for an interaction localized on the boundary of their 1+1 dimensional world. The boundary action is the sum of two pieces: a periodic potential and a coupling to a…
In this paper, we prove four-moment theorems for multidimensional free Poisson limits on free Wigner chaos or the free Poisson algebra. We prove that, under mild technical conditions, a bi-indexed sequence of free stochastic integrals in…
A class of improved estimators is proposed for N-point correlation functions of galaxy clustering, and for discrete spatial random processes in general. In the limit of weak clustering, the variance of the unbiased estimator converges to…