LX growth distribution

Determine whether the LX growth distribution has a limiting Gumbel distribution as n tends to infinity, and establish the conjectured asymmetry and kurtosis bounds.

Background

Computations for the LX generators suggest a non-Gaussian, asymmetric growth distribution that may be approximated by a Gumbel law. The authors explicitly caution that the available empirical skewness and kurtosis data do not yet settle the limiting behavior.

References

It might be also that the distribution tends to the Gumbel one when $n\to \infty$, however that is not completely clear since empiric skew and kurt are not well fitted (however it might be an effect of small $n$).

— CayleyPy Growth: Efficient growth computations and hundreds of new conjectures on Cayley graphs (Brief version)  (2509.19162 - Chervov et al., 23 Sep 2025) in Section 12, subsection “Further results and conjectures on growth”