Spacings and pair correlations for finite Bernoulli convolutions
Spacings and pair correlations for finite Bernoulli convolutions
复制标题
有限伯努利卷积的间距和对相关性
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
B. Solomyak
中科院分区：
文献类型：
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作者：
I. Benjamini;B. Solomyak
我们考虑离散点集上参数为1/2<；λ<；1的有限Bernoulli卷积，一般大小为2N。这些序列关于无限伯努利卷积测度νλ是均匀分布的，为N→∞。数值证据表明，对于一般的λ，适当重新标度的点之间的间距分布是泊松的。我们在这个方向上得到了一些部分结果；例如，我们证明了，平均而言，对关联在极限上不表现出吸引或排斥。另一方面，对于某些代数λ，其行为是完全不同的。
We consider finite Bernoulli convolutions with a parameter 1/2 < λ < 1 supported on a discrete point set, generically of size 2N. These sequences are uniformly distributed with respect to the infinite Bernoulli convolution measure νλ, as N → ∞. Numerical evidence suggests that for a generic λ, the distribution of spacings between appropriately rescaled points is Poissonian. We obtain some partial results in this direction; for instance, we show that, on average, the pair correlations do not exhibit attraction or repulsion in the limit. On the other hand, for certain algebraic λ the behaviour is totally different.