Characterizing spatial point processes by percolation transitions
arXiv:2206.04483 · doi:10.1088/1742-5468/ac7a2c
Abstract
A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical ecology to analyze, e.g., the spatial percolation of a tree species in a tropical forest or a savanna. Here, we revisit the problem of aggregating random points in continuum systems (from to dimensional Euclidean spaces) to analyze the nature of the corresponding percolation transition in spatial point processes. This problem finds a natural description in terms of the canonical ensemble but not in the usual grand-canonical one, customarily employed to describe percolation transitions. This leads us to analyze the question of ensemble equivalence and study whether the resulting canonical continuum percolation transition shares its universal properties with standard percolation transitions, analyzing diverse homogeneous and heterogeneous spatial point processes. We, therefore, provide a powerful tool to characterize and classify a vast class of natural point patterns, revealing their fundamental properties based on percolation phase transitions.
arXiv comment22 pages, 13 figures
References in corpus (36)
- Epidemic processes in complex networks
- Universality classes in nonequilibrium lattice systems
- A fast Monte Carlo algorithm for site or bond percolation
- Random Geometric Graphs
- Entropy measures for complex networks: Toward an information theory of complex topologies
- Percolation on sparse networks
- Percolation in Directed Scale-Free Networks
- Continuum Percolation Thresholds in Two Dimensions
- Avalanche and spreading exponents in systems with absorbing states
- Percolation of localized attack on complex networks
- Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
- The continuum percolation threshold for interpenetrating squares and cubes
- Explosive percolation: a numerical analysis
- Continuum percolation of wireless ad hoc communication networks
- A Generalized Epidemic Process and Tricritical Dynamic Percolation
- Numerical Determination of the Avalanche Exponents of the Bak-Tang-Wiesenfeld Model
- Breaking of ensemble equivalence in networks
- Gibbs entropy of networks ensembles by cavity methods
- Convergence of threshold estimates for two-dimensional percolation
- Point processes and stochastic displacement fields
- Effect of Dimensionality on the Continuum Percolation of Overlapping Hyperspheres and Hypercubes: II. Simulation Results and Analyses
- A simple unified view of branching process statistics: random walks in balanced logarithmic potentials
- Percolation in real Wildfires
- Percolation and the pandemic
- Mean-field behavior of the sandpile model below the upper critical dimension
- On the scaling of probability density functions with apparent power-law exponents less than unity
- Percolation in the canonical ensemble
- Surface Hardening and Self-Organized Fractality Through Etching of Random Solids
- No-enclave percolation corresponds to holes in the cluster backbone
- Classes of critical avalanche dynamics in complex networks
- Field theory of self-organized fractal etching
- Non equivalence of dynamical ensembles and emergent non ergodicity
- Joint assessment of density correlations and fluctuations for analysing spatial tree patterns
- Emergent spatial patterns of coexistence in species-rich plant communities
- Percolation theory of self-exciting temporal processes
- Island and lake size distributions in Gradient Percolation