Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 3, pp. 331--338

A NOTE ON WEAK-* PERTURBATIONS OF *g*-MEASURES

By

Y. LACROIX, *Université de Picardie Jules Verne,
France*

*SUMMARY. *We observe that the standard Kemeny
and Snell identity, basic in Markov Chain Perturbation Theory,
generalizes to chains with complete connections. Therefrom a few
elementary observations are derived for weak-*
perturbation of *g*-measures considered as a function of
*g*.
This identity is applied to produce a simple proof for the phase
transition phenomenon recently exhibited in Bramson and Kalikow (1993).

*AMS (1991) subject classification. *28D05, 41A80, 47A35, 60J10, 60J35,
82B30.

*Key words and phrases. *Kemeny and Snell identity,
chains with complete connections, local perturbations, phase
transition, uniqueness.