Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ergodicity of the Martin boundary of the Young--Fibonacci graph. I   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 prove the
statements which correspond to the case $\beta=1$.

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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph