A Markov process associated with plot-size distribution in Czech Land Registry and its number-theoretic properties

TL;DR

This paper models land plot size distribution in the Czech Land Registry as a Markov process, revealing connections to number theory and the Dickman function, with implications for understanding land allocation patterns.

Contribution

It introduces a Markov process model for land plot sizes and links the distribution of garden plots to prime number factorization, a novel interdisciplinary approach.

Findings

Distribution of garden plots matches Dickman function predictions.

Build-up areas show similar probabilistic characteristics.

Supports the Markov process as a valid model for land distribution patterns.

Abstract

The size distribution of land plots is a result of land allocation processes in the past. In the absence of regulation this is a Markov process leading an equilibrium described by a probabilistic equation used commonly in the insurance and financial mathematics. We support this claim by analyzing the distribution of two plot types, garden and build-up areas, in the Czech Land Registry pointing out the coincidence with the distribution of prime number factors described by Dickman function in the first case.