Information Percolation: Some General Cases with an Application to Econophysics

TL;DR

This paper analyzes the microscopic dynamics of large interacting systems with rare interactions, derives explicit solutions for the macroscopic differential equations, and applies these findings to models in Econophysics.

Contribution

It provides a general framework for understanding interaction dynamics in large systems and offers explicit solutions, with applications to Econophysics models.

Findings

Explicit formula for the solution of the quadratic differential system.

Demonstration of the negligible probability of multiple interactions in large systems.

Application of the theoretical results to Econophysics models.

Abstract

We describe, at the microscopic level, the dynamics of N interacting components where the probability is very small when N is large that a given component interact more than once, directly or indirectly, up to time t, with any other component. Due to this fact, we can consider, at the macroscopic level, the quadratic system of differential equations associated with the interaction and establish an explicit formula for the solution of this system. We moreover apply our results to some models of Econophysics.