Related papers: Limit theorems for a general stochastic rumour mod…
We consider a rumor model in which the network is divided into three classes of agents: ignorant, spreader, and stifler. A spreader transmits the rumor to each of its ignorant neighbors at rate one, and at the same rate, it becomes a…
We introduce a non-Markovian rumor model on a complete graph of $n$ vertices, integrating the classical interactional framework of Daley and Kendall (1964) with modern cognitive insights into misinformation. Unlike traditional Markovian…
We study a stochastic model for the diffusion of competing opinions in a population composed of three types of agents: trend-followers, opposers, and indifferent individuals. The decision dynamics are driven by reinforcement mechanisms,…
The burst in the use of online social networks over the last decade has provided evidence that current rumor spreading models miss some fundamental ingredients in order to reproduce how information is disseminated. In particular, recent…
We study a rumor spreading model where individuals are connected via a network structure. Initially, only a small subset of the individuals are spreading a rumor. Each individual who is connected to a spreader, starts spreading the rumor…
In this work we propose a new extension for the Maki-Thompson rumor model which incorporates inter-group directed contacts. The model is defined on an homogeneously mixing population where the existence of two differentiated groups of…
We study the diffusion of a true and a false message (the rumor) in a social network. Upon hearing a message, individuals may believe it, disbelieve it, or debunk it through costly verification. Whenever the truth survives in steady state,…
The dynamics of fake news and rumor spreading is investigated using a model with three kinds of agents who are respectively the Seeds, the Agnostics and the Others. While Seeds are the ones who start spreading the rumor being adamantly…
In this paper, under mild assumptions, we derive a law of large numbers, a central limit theorem with an error estimate, an almost sure invariance principle and a variant of Chernoff bound in finite-state hidden Markov models. These limit…
In this paper we propose a deterministic mathematical model that attempts to explain the propagation of a rumor using SIRS type epidemiological models with temporary immunity and nonlinear incidence rate. In particular, we speculate about…
This paper examines the quasi-stationary behavior of stochastic rumor processes. Using the results by van Doorn and Pollett (2008), we first prove that the continuous-time Maki--Thompson model has a unique quasi-stationary distribution…
The spread of ideas in online social networks is a crucial phenomenon to understand nowadays the proliferation of fake news and their impact in democracies. This makes necessary to use models that mimic the circulation of rumors. The law of…
We study two rumor processes on $\N$, the dynamics of which are related to an SI epidemic model with long range transmission. Both models start with one spreader at site $0$ and ignorants at all the other sites of $\N$, but differ by the…
The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…
Rumor and information spreading are natural processes that emerge from human-to-human interaction. Mathematically, this was explored in the popular Maki-Thompson model, where a phase transition was thought to be absent. Here, we show that a…
Consider informative selection of a sample from a finite population. Responses are realized as independent and identically distributed (i.i.d.) random variables with a probability density function (p.d.f.) f, referred to as the…
Growing literatures on epidemic and rumor dynamics show that infection and information coevolve. We present a unified framework for modeling the spread of infection and information: a general class of interaction-driven fluid-limit models…
We develop original models to study interacting agents in financial markets and in social networks. Within these models randomness is vital as a form of shock or news that decays with time. Agents learn from their observations and learning…
The spread of rumors, which are known as unverified statements of uncertain origin, may cause tremendous number of social problems. If it would be possible to identify factors affecting spreading a rumor (such as agents' desires, trust…
Rumor models consider that information transmission occurs with the same probability between each pair of nodes. However, this assumption is not observed in social networks, which contain influential spreaders. To overcome this limitation,…