Random Walks with Anti-Correlated Steps

TL;DR

This paper conjectures that the expected value of anti-correlated random walks is exactly 1, supported by plausibility arguments and experimental data showing convergence up to 22 steps.

Contribution

It introduces a conjecture about the expected value of anti-correlated random walks and provides empirical evidence and plausibility arguments to support it.

Findings

Expected value converges to 1 asymptotically

Experimental data up to 22 steps supports the conjecture

Provides plausibility arguments for the conjecture

Abstract

We conjecture the expected value of random walks with anti-correlated steps to be exactly 1. We support this conjecture with 2 plausibility arguments and experimental data. The experimental analysis includes the computation of the expected values of random walks for steps up to 22. The result shows the expected value asymptotically converging to 1.