Moderate deviations for the Maki--Thompson rumour model

TL;DR

This paper establishes the moderate deviation principle for the final proportion of ignorants in the Maki--Thompson rumour model, connecting Gaussian fluctuations and large deviations.

Contribution

It introduces the moderate deviation principle for the model, extending the understanding of its probabilistic behavior beyond existing laws.

Findings

Proves the moderate deviation principle for the model.

Provides sharp asymptotics for automata numbers.

Uses exact final-size distribution and point probability expansion.

Abstract

The final proportion of ignorants in the classical Maki--Thompson rumour model is known to satisfy the law of large numbers, the central limit theorem, and the large deviation principle. In this note, we establish the corresponding moderate deviation principle, thereby bridging the Gaussian fluctuation regime and the large deviation regime. The proof rests on the exact final-size distribution, sharp asymptotics for the associated automata numbers, and a uniform point probability expansion at the moderate deviation scale.