Infinite-Scale Percolation in a New Type of Branching Diffusion Processes

TL;DR

This paper introduces a new class of stochastic processes combining percolation theory and branching diffusion, providing insights into infinite-scale percolation phenomena.

Contribution

It presents a novel type of branching process with diffusion on parameter spaces, bridging percolation theory and diffusion processes.

Findings

Development of a new stochastic process model.

Insights into infinite-scale percolation behavior.

Potential applications in complex systems modeling.

Abstract

We give an account of matter and (basically) a solution of a new class of problems synthesizing percolation theory and branching diffusion processes. They led us to realizing a novel type of stochastic processes, namely branching processes with diffusion on the space of parameters distinguishing the branching `particles' each other.