Laws of the single logarithm for delayed sums of random fields

TL;DR

This paper extends the law of the single logarithm to delayed sums of random fields, providing a new theoretical result that generalizes previous one-dimensional cases and subsequence laws.

Contribution

It introduces a generalized law of the single logarithm for delayed sums in random fields, expanding the theoretical framework beyond prior one-dimensional results.

Findings

Law established for random fields with delayed sums

Includes subsequence results and one-dimensional cases

Advances theoretical understanding of logarithmic laws

Abstract

We extend a law of the single logarithm for delayed sums by Lai to delayed sums of random fields. A law for subsequences, which also includes the one-dimensional case, is obtained in passing.