The continuous-time frog model can spread arbitrarily fast

TL;DR

This paper proves that in the continuous-time frog model, the spread of activity can occur at arbitrarily high speeds, with the set of visited sites becoming infinite in finite time.

Contribution

It demonstrates that the continuous-time frog model can spread infinitely fast, a significant departure from previous models with bounded spreading speeds.

Findings

The model can reach infinitely many sites in finite time.

Spreading speed is unbounded in the continuous-time setting.

The set of visited sites can become infinite instantly.

Abstract

The aim of this work is to demonstrate that the continuous-time frog model can spread arbitrary fast. The set of sites visited by an active particle can become infinite in a finite time.