Multiscaling in the sequence of areas enclosed by coalescing random walkers

TL;DR

This paper investigates the multiscaling behavior of the sequence of areas between coalescing random walkers, providing exact calculations and numerical estimates that confirm multiscaling properties through analytical and computational methods.

Contribution

It offers the first exact calculations of the second moment and correlation functions for this system, demonstrating multiscaling with numerical support.

Findings

Exact second moment and correlation functions calculated

Numerical estimates suggest logarithmic size dependence

Evidence confirms the presence of multiscaling in the system

Abstract

We address the question whether the sequence of areas between coalescing random walkers displays multiscaling and in the process calculate the second moment as well as the two point correlation function exactly. The scaling of higher order correlation functions is estimated numerically, indicating a logarithmic dependence on the system size. Together with the analytical results, this confirms the presence of multiscaling.