Extremality of Disordered Phase of λ-Model on Cayley Trees
Farrukh MukhamedovDepartment of Algebra and Analysis, Institute of Mathematics Named after V.I.Romanovski, 4, University Str., Tashkent 100125, Uzbekistan
2022en
ABI
Abstract
In this paper, we consider the λ-model for an arbitrary-order Cayley tree that has a disordered phase. Such a phase corresponds to a splitting Gibbs measure with free boundary conditions. In communication theory, such a measure appears naturally, and its extremality is related to the solvability of the non-reconstruction problem. In general, the disordered phase is not extreme; hence, it is natural to find a condition for their extremality. In the present paper, we present certain conditions for the extremality of the disordered phase of the λ-model.
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