Cell size distribution in random tessellations of space

Area of Science:

• Multidisciplinary applications of spatial statistics
• Computational geometry and stochastic processes

Background:

• Random space subdivisions are prevalent in diverse scientific fields like materials science, geology, and biology.
• Understanding the statistical properties of these subdivisions, particularly cell size distribution, is crucial for modeling and analysis.
• Existing models often focus on specific random point processes, limiting general applicability.

Purpose of the Study:

• To develop an analytical approximation for the size probability distribution of cells in random space subdivisions.
• To provide a generalized method applicable to various random cellular structures, including Poisson-Voronoi and Johnson-Mehl tessellations.
• To enhance the understanding of geometric probability in high-dimensional spaces.

Main Methods:

• Analytical approximation based on established statistical calculations (Ann. Math. Stat. 33, 958).
• Incorporation of an assumption regarding the shape of the size distribution.
• Generalization of methods to encompass a wide range of random space subdivision models.

Main Results:

• An analytical approximation for the cell size probability distribution is derived.
• The method is shown to be applicable to well-known structures like Poisson-Voronoi and Johnson-Mehl cells.
• A general framework for analyzing random cellular structures is established.

Conclusions:

• The presented analytical approximation offers a versatile tool for studying random space subdivisions.
• This work extends the understanding of cell size distributions in stochastic geometry.
• The generalized approach facilitates analysis across multiple scientific domains utilizing random tessellations.