Related papers: Poissonian bursts in e-mail correspondence
Within a Monte Carlo simulation we investigate the statistical properties of an electron flow injected with a Poissonian distribution and transmitted under ballistic regime in the presence of long-range Coulomb interaction. Electrons are…
Interevent times in temporal contact data from humans and animals typically obey heavy-tailed distributions, and this property impacts contagion and other dynamical processes on networks. We theoretically show that distributions of…
The full counting statistics of a molecular level weakly interacting with a local phonon mode is derived. We find an analytic formula that gives the behavior of arbitrary irreducible moments of the distribution upon phonon excitation. The…
Event occurrence is not only subject to the environmental changes, but is also facilitated by the events that have occurred in a system. Here, we develop a method for estimating such extrinsic and intrinsic factors from a single series of…
In multitasking operating systems, requests for free memory are traditionally modeled as a stochastic counting process with independent, exponentially-distributed interarrival times because of the analytic simplicity such Poisson models…
Widespread interest in the diffusion of information through social networks has produced a large number of Social Dynamics models. A majority of them use theoretical hypothesis to explain their diffusion mechanisms while the few empirically…
A common assumption when modeling queuing systems is that arrivals behave like a Poisson process with constant parameter. In practice, however, call arrivals are often observed to be significantly overdispersed. This motivates that in this…
We present a mathematical model for communication subject to both network interference and noise. We introduce a framework where the interferers are scattered according to a spatial Poisson process, and are operating asynchronously in a…
The result provided in this paper helps complete a unified picture of the scaling behavior in heavy-tailed stochastic models for transmission of packet traffic on high-speed communication links. Popular models include infinite source…
Consider two independent Poisson point processes of unit intensity in the Euclidean space of dimension $d$ at least 3. We construct a perfect matching between the two point sets that is a factor (i.e., an equivariant measurable function of…
The Poisson probability distribution is frequently encountered in physical science measurements. In spite of the simplicity and familiarity of this distribution, there is considerable confusion among physicists concerning the description of…
A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials,…
Solar flares, email exchanges, and many natural or social systems exhibit bursty dynamics, with periods of intense activity separated by long inactivity. These patterns often follow power- law distributions in inter-event intervals or event…
We review the decomposition method of stock return cross-correlations, presented previously for studying the dependence of the correlation coefficient on the resolution of data (Epps effect). Through a toy model of random walk/Brownian…
We consider a one-dimensional gas of $N$ independent Brownian particles subject to simultaneous stochastic resetting, with inter-reset times drawn from a general waiting-time distribution $\psi(\tau)$. This includes the well-known…
Neural computations arising from myriads of interactions between spiking neurons can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this…
We experimentally study a gas of $N = 8$ one-dimensional Brownian particles, each confined in a harmonic trap with identical stiffness. The stiffness switches simultaneously between two values at random Poissonian times. This collective…
Human social interactions tend to vary in intensity over time, whether they are in person or online. Variable rates of interaction in structured populations can be described by networks with the time-varying activity of links and nodes. One…
We derive an analytical approximation to the probability distribution function (pdf) for the response of Mathieu's equation under parametric excitation by a random process with a spectrum peaked at the main resonant frequency, motivated by…
As a first step toward a characterization of the limiting extremal process of branching Brownian motion, we proved in a recent work [Comm. Pure Appl. Math. 64 (2011) 1647-1676] that, in the limit of large time $t$, extremal particles…