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arXiv · 1909.05837

Estimation of expected value of function of i.i.d. Bernoulli random variables

March T. Boedihardjo
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Abstract

We estimate the expected value of certain function $f:\{-1,1\}^{n}\to\mathbb{R}$. For example, with computer assistance, we show that if $\Delta$ is the Laplacian of the Cayley graph of $(\mathbb{Z}/15\mathbb{Z})\times(\mathbb{Z}/15\mathbb{Z})$ and $D$ is a diagonal $225\times 225$ matrix with entries chosen independently and uniformly from $\{-1,1\}$, then the expected value of the normalized trace of $(2I+D-\Delta)^{-1}$ is between $0.2006$ and $0.2030$.

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March T. Boedihardjo. 2019-09-12. Estimation of expected value of function of i.i.d. Bernoulli random variables. https://arxiv.org/abs/1909.05837

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