The one-site distribution of Gibbs states on Bethe lattice are probability vectors of period≤2 for a nonlinear transformation

Eric Goles, Servet Martinez

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

2 Citas (Scopus)

Resumen

We prove that the one-site distribution of Gibbs states (for any finite spin set S) on the Bethe lattice is given by the points satisfying the equation π=T2π, where T=h·A·φ{symbol}, with φ{symbol}(x)=x(q-1/q, h(x)=(x∥x∥q)q, A=(a(r, s):r, s∈S), and {Mathematical expression} We also show that for A a symmetric, irreducible operator the nonlinear evolution on probability vectors x(n+1)=Ax(n)p∥Ax(n)p1 with p>0 has limit points ξ of period≤2. We show that A positive definite implies limit points are fixed points that satisfy the equation Aξp=λξ. The main tool is the construction of a Liapunov functional by means of convex analysis techniques.

Idioma originalInglés
Páginas (desde-hasta)267-285
Número de páginas19
PublicaciónJournal of Statistical Physics
Volumen52
N.º1-2
DOI
EstadoPublicada - jul. 1988
Publicado de forma externa

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