The article is devoted to the development and testing of a theoretical and methodological approaches to studying the dynamics of spatial inequality using probabilistic modeling of time intervals. Unlike traditional statistical methods that capture the state of a system in statics, the proposed approach allows assessing the duration of regions' stay within specified economic stability parameters and calculating the probability of their deviation from the national development trajectory. The key stability indicator is the time until a "divergence event" occurs — when the real per capita income of a region moves beyond established threshold values relative to the media. Based on an analysis of panel data 2011–2023 for Russian regions, the authors constructed probabilistic models for three levels of divergence (mild, moderate, and strong). The research results demonstrate a progressive erosion of the "core" of the regional system: the share of territories maintaining a state of low divergence decreased from 75% in 2011 to 60% by 2023. The identified patterns indicate a structural shift of the regional system from a relatively homogeneous distribution toward pronounced polarization and stratification. The proposed methodology can be integrated into the regional project management system for monitoring systemic risks and assessing the long-term stability of the socio-economic space.
Dubovik et al. (Mon,) studied this question.
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