Statistical Language Competition Model with Dynamic Edge Weighting on a Random Network
Abstract
This paper presents a computational study of language competition dynamics on Erdős--Rényi 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 Δ, 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 $(p, Δ)$, 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 ∈ {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.
Related
- Mass weighting algorithm optimizes Fourier-based physics-informed neural network in adhesive contact mechanics
- A Dynamic Model of Party Differentiation under Electoral Competition
- A gradient-enhanced physics-informed neural network with adaptive loss weighting for high-dimensional non-linear sine-Gordon problems
- Statistical physics of language change inferred from time evolving maps
- The Nonlinear Physics and Statistical Field Theory of Twilight Clouds: Hovering Dynamics and Dynamic Inertia Emergence
BibTeX
@misc{chakra2026statistical,
title = {{Statistical Language Competition Model with Dynamic Edge Weighting on a Random Network}},
author = {Somyaranjan Chakra and Mohit Anand Madhesia and Shradha Mishra},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01078},
eprint = {2609.01078},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01078},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Statistical Language Competition Model with Dynamic Edge Weighting on a Random Network
AU - Somyaranjan Chakra
AU - Mohit Anand Madhesia
AU - Shradha Mishra
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.01078
UR - https://arxiv.org/abs/2609.01078
AB - This paper presents a computational study of language competition dynamics on Erdős--Rényi 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 Δ, 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 $(p, Δ)$, 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 ∈ {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.
ER -