Symmetric Structure in Spatial and Social Processes

M Batty and K J Tinkler
Additional contact information
M Batty: Department of Geography, University of Reading, Whiteknights, Reading RG6 2AB, England
K J Tinkler: Department of Geography, Brock University, Saint Catharines, Ontario LS2 3A1, Canada

Environment and Planning B, 1979, vol. 6, issue 1, 3-27

Abstract: This paper presents an exploration into the effect of symmetric structure on the equilibrium properties of a widely applied class of ergodic Markov processes. An initial discussion of the notions concerning structure and process in this context sets the scene for the statement and proof of a simple theorem relating structures with a symmetry property to their associated steady-state relationships. The theorem has implications for models which arise in many disciplines. Symmetric structures and their related interpretation in terms of reversible processes occur in a variety of fields, and thus a series of examples pertaining to the spatial and social realms are used to illustrate these implications. The examples involve: access in spatial systems, diffusion based on random walks in spatial structures, economic exchange and equilibrium, social power and conflict resolution, design method in architecture and planning, and collective action in social systems. The themes running through all of these examples relate to balanced or equal movement, diffusion, exchange, or communication, which all imply reversible processes. The logic of the theorem is reinforced by each of these examples in intuitive terms, and by way of conclusion the many implications emerging from this analysis suggest directions for future research.

Date: 1979
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://journals.sagepub.com/doi/10.1068/b060003 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:sae:envirb:v:6:y:1979:i:1:p:3-27

DOI: 10.1068/b060003

Access Statistics for this article

More articles in Environment and Planning B
Bibliographic data for series maintained by SAGE Publications ().