p-Adic distribution of CM points and Hecke orbits. II: Linnik equidistribution on the supersingular locus

For every prime number $p$, this paper determines the asymptotic distribution of CM points on the moduli space of elliptic curves over $\mathbb{C}_p$. In stark contrast to the complex case, the $p$-adic setting admits infinitely many distinct accumulation measures. The paper identifies all such meas