Related papers: Self-organized model of cascade spreading

We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…

Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information…

We consider a system of $N$ interacting particles, described by SDEs driven by Poisson random measures, where the coefficients depend on the empirical measure of the system. Every particle jumps with a jump rate depending on its position.…

Spreading processes are ubiquitous in natural and artificial systems. They can be studied via a plethora of models, depending on the specific details of the phenomena under study. Disease contagion and rumor spreading are among the most…

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks…

We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a…

Plastic deformation of crystalline and amorphous matter often involves intermittent local strain burst events. To understand the physical background of the phenomenon a minimal stochastic mesoscopic model was introduced, where…

The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…

Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in…

Power law distribution seems to be an important characteristic of web graphs. Several existing web graph models generate power law graphs by adding new vertices and non-uniform edge connectivities to existing graphs. Researchers have…

Threshold rules of spreading in binary-state networks lead to cascades. We study persistent cascade-recovery dynamics on quasi-robust networks, i.e., networks which are robust against small trigger but may collapse for larger one. It is…

We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness…

We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…

A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical…

In this paper I propose a 'mechanism' for the explanation of power-law characteristics of casualty dynamics in inter-state wars, intra-state wars and terrorist attacks: the scale-free physical organization of social systems. Other…

Stochastic spreading models defined on complex network topologies are used to mimic the diffusion of diseases, information, and opinions in real-world systems. Existing theoretical approaches to the characterization of the models in terms…

Cascades on random networks are typically analyzed by assuming they map onto percolation processes and then are solved using generating function formulations. This approach assumes that the network is infinite and weakly connected, yet…

We investigate the mechanisms behind the power-law distribution of stock returns using artificial market simulations. While traditional financial theory assumes Gaussian price fluctuations, empirical studies consistently show that the tails…

An analytical study of the return time distribution of extreme events for stochastic processes with power-law correlation has been carried on. The calculation is based on an epsilon-expansion in the correlation exponent:…

Network data appear in a number of applications, such as online social networks and biological networks, and there is growing interest in both developing models for networks as well as studying the properties of such data. Since individual…