Statistical field theory for dialectology.

Area of Science:

• Computational Linguistics
• Statistical Physics
• Sociolinguistics

Background:

• Existing models lack the spatial-temporal detail to track historical linguistic changes at the feature level.
• There's a need for a principled mechanism to predict future language evolution.
• Statistical physics offers promising approaches but requires a comprehensive model.

Purpose of the Study:

• To develop a "physics of language" capable of explaining and predicting linguistic patterns.
• To introduce a statistical field theory for linguistic variable evolution.
• To provide a model that matches historical changes and predicts future shifts.

Main Methods:

• Representing linguistic variant frequencies as a stochastic state field with spatial and social interactions.
• Coupling the state field to a latent bias field using Onsager-Machlup action to minimize data overfitting.
• Deriving parameter inference procedures and applying them to 20th-century US dialect survey data.

Main Results:

• The statistical field theory successfully models linguistic variant frequencies and their evolution.
• The model's bias field exhibits a characteristic half-life, defining the predictability horizon for linguistic change.
• Inferred parameters suggest surface-tension-driven coarsening of dialect regions influenced by population density gradients.

Conclusions:

• The developed statistical field theory provides a novel framework for understanding language evolution.
• The model offers a principled mechanism for predicting future linguistic changes.
• The findings reveal insights into dialect region dynamics and the forces shaping linguistic interfaces.