论文标题
年轻的 - 菲比诺奇图的马丁边界的成真。我
Ergodicity of the Martin boundary of the Young--Fibonacci graph. I
论文作者
论文摘要
在年轻的路径空间中的中心措施中，即所谓的planchel措施具有特殊的作用。 Kerov和Gnedin证明了它的成真性。这两篇文章的这一循环的目的是证明该图的马丁边界的其余措施（由Kerov和Goodman描述）也是ergodic。这些度量用无限的数字1和2词进行了参数化，并且参数$β\ in（0,1] $（情况$β= 0 $）对应于Plancherel量度）。在本文中，我们证明了与情况$β= 1 $相对应的陈述。
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 $β\in(0,1]$ (the case $β=0$ corresponds to the Plancherel measure). In this article we prove the statements which correspond to the case $β=1$.
