  We study the fluctuation theory analysis of multiple soft interactions that
are used to design SIBYLL 2.1 and related cosmic ray event generators. We
examine fluctuation stabilities of Lund string fragmentation involving
quark-antiquark and diquark-antidiquark pairs. Using the primordial transverse
momentum hadron-hadron pairs, we find that the resulting Gaussian distribution
yields an ill-defined ensemble under fluctuation of the model parameters of
parent quark and diquarks. Further, we investigate the nature of multiple soft
interactions through Pomeron-Reggeon fluctuations at various energy scales. We
show that there are both stable and unstable regions under fluctuations of the
Reggeon and Pomeron densities and all initial energy scales. The optimal
stability zone is achieved at the Reggeon and Pomeron densities as predicted by
GRV model. For hadron-hadron collisions, the limiting Gaussian profile as a
function of the impact parameters of soft interactions for proton-proton
collisions corresponds to an indeterminate statistical basis. Subsequently, we
add higher order corrections in the Regge trajectory of constituent hadrons
that play an important role in determining the shape of a proton or meson
profile function in the realm of minijet model. We also discuss the accelerated
nucleons with jerks and soft profile functions at off-shell-conditions. In
addition, we illustrate the wall of stability/instability for multiple soft
interactions by considering energy dependent soft contributions to scattering
cross section as the model embedding. Qualitative discussions are provided at
physical energy scales ranging from 1 GeV to 1800 GeV. This includes the
analysis of CDF, P238, UA5 and ZEUS experiments.
