Statistical Language Competition Model with Dynamic Edge Weighting on a Random Network

Abstract

This paper presents a computational study of language competition dynamics on Erd\H{o}s--R\'enyi random networks, extending the foundational Abrams--Strogatz model through two novel contributions: (i) a dynamic edge-weighting mechanism that reinforces social ties between co-minority speakers by an additive increment $\Delta$, and (ii) a probabilistic agent-based framework governing language switching via a weighted majority rule. Phase boundaries separating the dominance and coexistence regimes are identified across a two-dimensional parameter space $(p, \Delta)$, where $p$ denotes the network connectivity probability. We further characterise anomalous persistence zones within predicted dominance regions, attributing them to the formation of isolated minority speaker clusters. Scaling study across network sizes $N \in \{50, 100, 250, 500, 1000\}$ reveal that average cluster size decreases with $N$ and that phase boundaries diffuse with increasing stochastic noise. Finally, we discuss extensions to a tripartite bilingual model and heterogeneous prestige/volatility to more faithfully capture real sociolinguistic contact scenarios.