Delta-Cumulants in terms of moments

Josuat-Verges Matthieu

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Delta-Cumulants in terms of moments

机译：三角形累积剂在时刻

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摘要

The Delta-convolution of real probability measures, introduced by Bolejko, generalizes both free and Boolean convolutions. It is linearized by the Delta-cumulants, and Yoshida gave a combinatorial formula for moments in terms of Delta-cumulants, that implicitly defines the latter. It relies on the definition of an appropriate weight on noncrossing partitions. We give here two different expressions for the Delta-cumulants: the first one is a simple variant of Lagrange inversion formula, and the second one is a combinatorial inversion of Yoshida's formula involving Schroder trees.

机译：Bolejko引入的实际概率措施的三角洲卷积概括了免费和布尔卷曲。它由三角形累积物线性化，尤达达在δ累积物方面为矩的组合公式进行了瞬间，其隐含地定义了后者。它依赖于对非交易分区的适当重量的定义。我们在这里给出了两种不同的表达式，即三角形累积物：第一个是拉格朗日反转公式的简单变体，第二个是尤达达公式的组合反演，涉及施罗德树。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2018年第2期|共16页
作者
Josuat-Verges Matthieu;
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作者单位

CNRS Champs Sur Marne France;

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原文格式 PDF
正文语种 eng
中图分类物理学;
关键词
Convolutions; Schroder trees; noncrossing partitions;

机译：卷积;斯科罗树;非交叉分区;

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Delta-Cumulants in terms of moments

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