# Ordering statistics of 4 random walkers on the line.

We study the ordering statistics of 4 random walkers on the line, obtaining a much improved estimate for the long-time decay exponent of the probability that a particle leads to time $t$; $P_{\rm lead}(t)\sim t^{-0.91287850}$, and that a particle lags to time $t$ (never assumes the lead); $P_{\rm lag}(t)\sim t^{-0.30763604}$. Exponents of several other ordering statistics for $N=4$ walkers are obtained to 8 digits accuracy as well. The subtle correlations between $n$ walkers that lag {\em jointly}, out of a field of $N$, are discussed: For $N=3$ there are no correlations and $P_{\rm lead}(t)\sim P_{\rm lag}(t)^2$. In contrast, our results rule out the possibility that $P_{\rm lead}(t)\sim P_{\rm lag}(t)^3$ for $N=4$, though the correlations in this borderline case are tiny.

Publisher URL: http://arxiv.org/abs/1801.03453

DOI: arXiv:1801.03453v1

Researcher is an app designed by academics, for academics. Create a personalised feed in two minutes.

Choose from over 15,000 academics journals covering ten research areas then let Researcher deliver you papers tailored to your interests each day.

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.