The goal of the paper is to study limiting behavior Weierstrass measures on a smooth curve genus $g \geqslant 2$ as approaches certain nodal stable represented by point in Deligne–Mumford compactification $\overline{\mathcal{M}}_g$ moduli $\mathcal{M}_g$, including irreducible ones or those compact type. As consequence, rational at boundary $\mathcal{M}_g$ are completely determined. In process,...

We derive the representative Bernstein measure of the density of (Xα), 0 < α < 1, where Xα is a positive stable random variable, as a Fox-H function. Up to a factor, this measure describes the law of some function aα of a uniform random variable U on (0,π). The distribution function of a1−α(U) is then expressed through a H-function and is used to describe more explicitly the density of the anal...

Abstract Subshifts of deterministic substitutions are ubiquitous objects in dynamical systems and aperiodic order (the mathematical theory quasicrystals). Two their most striking features that they have low complexity (zero topological entropy) uniquely ergodic. Random a generalisation where the substituted image letter is determined by Markov process. In stark contrast to counterparts, subshif...