1. On the degree of ultrametricity
- Author
-
J C Angles d'Auriac, R Rammal, and Benoît Douçot
- Subjects
Quantitative measure ,Pure mathematics ,Metric space ,Simple (abstract algebra) ,ESPACE ,General Engineering ,Combinatorial optimization problem ,Degree (angle) ,Ultrametric space ,Mathematics - Abstract
Using the notion of the subdominant ultrametric, the degree of ultrametricity of a given metric space (e.g. phase space) is introduced. A simple and efficient method for the calculation of is outlined. is shown to provide a simple quantitative measure of the deviation from exact ultrametricity. Explicit examples are used to illustrate this notion which is argued to be of some interest in statistical-mechanical models and combinatorial optimization problems La notion de degre d'ultrametricite d'un espace metrique donne est introduite a partir de l'ultrametrique sous-dominante. On decrit une procedure simple et efficace pour le calcul de . On montre que fournit une mesure quantitative simple de la deviation par rapport a l'ultrametricite exacte. Cette notion est illustree pour des exemples explicites et nous suggerons son interet dans les modeles de mecanique statistique ainsi que les problemes d'optimisation combinatoire
- Published
- 1985