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 2 to 6-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.

Characterizing spatial point processes by percolation transitions

Gili T.;
2022-01-01

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 2 to 6-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.
File in questo prodotto:
File Dimensione Formato  
Villegas_2022_J._Stat._Mech._2022_073202.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Copyright dell'editore
Dimensione 2.85 MB
Formato Adobe PDF
2.85 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
2206.04483.pdf

accesso aperto

Tipologia: Documento in Pre-print
Licenza: Creative commons
Dimensione 1.88 MB
Formato Adobe PDF
1.88 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/23299
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
social impact