双线性索引随机过程——完全提升插值的\emph{平稳化}

Mihailo Stojnic
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引用次数: 0

摘要

我们的论文\cite{Stojnicnflgscompyx23}为双线性索引随机过程引入了一个非常\emph{强大的提升}(fl)统计插值/比较机制。在这里,我们提出了这种机制的一个特殊实现,它依赖于沿插值路径概念的平稳化。在插值参数之间的非常基本的关系的集合被发现,上下文化,并提出。作为一个很好的奖励,在特殊的特殊情况下,我们表明,所引入的机器允许在实践中易于使用的形式的各种简化。考虑到有多少众所周知的随机结构和优化问题严重依赖于这里所考虑的类型的结果,应用范围几乎是无限的。我们也简要地指出其中的一些机会。
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Bilinearly indexed random processes -- \emph{stationarization} of fully lifted interpolation
Our companion paper \cite{Stojnicnflgscompyx23} introduced a very powerful \emph{fully lifted} (fl) statistical interpolating/comparison mechanism for bilinearly indexed random processes. Here, we present a particular realization of such fl mechanism that relies on a stationarization along the interpolating path concept. A collection of very fundamental relations among the interpolating parameters is uncovered, contextualized, and presented. As a nice bonus, in particular special cases, we show that the introduced machinery allows various simplifications to forms readily usable in practice. Given how many well known random structures and optimization problems critically rely on the results of the type considered here, the range of applications is pretty much unlimited. We briefly point to some of these opportunities as well.
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