Maximal entropy random walk improves efficiency of trapping in dendrimers

TL;DR

This paper demonstrates that maximal entropy random walk (MERW) significantly improves trapping efficiency in dendrimers modeled as Cayley trees, with a detailed analysis of mean first passage times and trapping times.

Contribution

The study provides explicit formulas for mean first passage time and average trapping time under MERW, revealing a much faster trapping process compared to unbiased random walks.

Findings

MERW reduces the average trapping time to scale as (ln N)^4

Explicit formulas for mean first passage time and average trapping time are derived

MERW outperforms unbiased random walk in trapping efficiency in dendrimers

Abstract

We use maximal entropy random walk (MERW) to study the trapping problem in dendrimers modeled by Cayley trees with a deep trap fixed at the central node. We derive an explicit expression for the mean first passage time from any node to the trap, as well as an exact formula for the average trapping time (ATT), which is the average of the source-to-trap mean first passage time over all non-trap starting nodes. Based on the obtained closed-form solution for ATT, we further deduce an upper bound for the leading behavior of ATT, which is the fourth power of $\ln N$, where $N$ is the system size. This upper bound is much smaller than the ATT of trapping depicted by unbiased random walk in Cayley trees, the leading scaling of which is a linear function of $N$. These results show that MERW can substantially enhance the efficiency of trapping performed in dendrimers.