On the length of the longest consecutive switches

TL;DR

This paper investigates the statistical properties of the longest sequence of consecutive switches in coin tosses, showing that its behavior parallels that of the longest head-run, providing insights into pattern lengths in random sequences.

Contribution

The paper establishes the limit behavior of the longest consecutive switches in coin tosses, extending understanding of pattern lengths in independent Bernoulli trials.

Findings

Limit behavior similar to longest head-run

Asymptotic distribution characterized

Provides theoretical foundation for pattern analysis

Abstract

An unbiased coin is tossed $n$ times independently and sequentially. In this paper, we will study the length of the longest consecutive switches, and prove that the limit behaviors are similar to that of the length of the longest head-run.