有限向量空间中的随机游走和 "欧几里得 "关联方案

Charles Brittenham, Jonathan Pakianathan
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引用次数: 0

摘要

在本文中,我们提供了有限平面中随机距离-t 步行的一个应用,并基于卡茨(N. Katz)建立的克洛斯特曼和的 "垂直 "等分布,推导出在 $\ell $ 步之后返回起点的概率的渐近公式(当 $q \to \infty $ 时)。这项工作依赖于 W. M. Kwok、E. Bannai、O. Shimabukuro 和 H. Tanaka 先前工作中研究的 "欧几里得 "关联方案。为方便应用,我们还提供了该方案的 P 矩阵和交集数的独立计算,以及平面情况下交集数的更明确形式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Random walks and the “Euclidean” association scheme in finite vector spaces

In this paper, we provide an application to the random distance-t walk in finite planes and derive asymptotic formulas (as $q \to \infty $) for the probability of return to start point after $\ell $ steps based on the “vertical” equidistribution of Kloosterman sums established by N. Katz. This work relies on a “Euclidean” association scheme studied in prior work of W. M. Kwok, E. Bannai, O. Shimabukuro, and H. Tanaka. We also provide a self-contained computation of the P-matrix and intersection numbers of this scheme for convenience in our application as well as a more explicit form for the intersection numbers in the planar case.

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