For every r>=2, the Martin boundary of the r-differential Young-Fibonacci graph is described explicitly by boundary words with a parameter beta, plus the Plancherel measure, and all these measures are ergodic.
Ergodicity of the Martin boundary of the Young--Fibonacci graph. II
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abstract
Among central measures on the path space of the Young--Fibonacci lattice the so-called Plancherel measure has a special role. Its ergodicity was proved by Kerov and Gnedin. The goal of this cycle of two articles is to prove that remaining measures from the Martin boundary of this graph (which were described by Kerov and Goodman) are also ergodic. The measures are parametrized with an infinite word of digits 1 and 2 and the parameter $\beta\in(0,1]$ (the case $\beta=0$ corresponds to the Plancherel measure). In this article we finish the proof of their ergodicity using the statements proved in the first paper as a "black box".
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Central measures on the r-differential version of the Young--Fibonacci graph
For every r>=2, the Martin boundary of the r-differential Young-Fibonacci graph is described explicitly by boundary words with a parameter beta, plus the Plancherel measure, and all these measures are ergodic.