Conjecture on the limiting distribution of the maximum degree as p tends to zero

Let $X$ denote the limiting random variable associated with the normalized maximum degree in Theorem 1.2, and let $D_1$ and $D_2$ be the constants appearing there. Maximum-degree limiting-distribution conjecture. When $p\rightarrow 0$, $X$ converges in distribution to a constant random variable. Equivalently, one may take $D_1=D_2$ in the statement of Theorem 1.2. The conjecture is motivated by the observation that, for each vertex $V_i$, the distribution of its degree at time $n$ resembles the degree distribution of the $\lfloor pi\rfloor$th vertex in a preferential attachment model with $pn$ vertices.