论文标题
最短暂的随机步行无限地削减时间
Most transient random walks have infinitely many cut times
论文作者
论文摘要
我们证明，如果$（x_n）_ {n \ geq 0} $是瞬态图上的随机步行，使得绿色的函数至少沿随机步行多个多样地衰减，则几乎可以肯定地肯定地固定了很多时间。此条件特别适用于严格大于$ 2 $的光谱维度图。实际上，我们的证明适用于马尔可夫链（可能是不可逆的）马尔可夫链，满足绿色功能的类似衰减条件，这对于出生死亡链而言是锋利的。我们推断出Diaconis和Freedman（Ann。probab。1980）的猜想是同一类马尔可夫链，并解决了本杰米尼，古雷尔·古里维奇（Gurel-Gurevich）和施拉姆（Ann。probab。2011）的猜想，这些猜测是无限的许多切割时间，以实现正速度的随机步行时间。
We prove that if $(X_n)_{n\geq 0}$ is a random walk on a transient graph such that the Green's function decays at least polynomially along the random walk, then $(X_n)_{n\geq 0}$ has infinitely many cut times almost surely. This condition applies in particular to any graph of spectral dimension strictly larger than $2$. In fact, our proof applies to general (possibly nonreversible) Markov chains satisfying a similar decay condition for the Green's function that is sharp for birth-death chains. We deduce that a conjecture of Diaconis and Freedman (Ann. Probab. 1980) holds for the same class of Markov chains, and resolve a conjecture of Benjamini, Gurel-Gurevich, and Schramm (Ann. Probab. 2011) on the existence of infinitely many cut times for random walks of positive speed.
