9 problems

Tail asymptotic conjecture. The same identity

The paper considers Theorems 1 and 2 concerning the existence and characterization of a self-similar measure-valued process and its associated Lamperti transformation. Generalizati…

Let $\mathbf{x}\in \ell^{\omega_-}_+\setminus\{\mathbf{0}\}$ be a sequence with infinitely many positive terms, and let $a(\mathbf{x},r)$ denote the density of…

The model considered in Samorodnitsky and collaborators' work is assumed to satisfy assumption (4.7), although the relevant particle-system setup is not specified here. Limit conje…

Persistence exponent conjecture. The process has persistence exponent $1-H$, meaning that

Let ${\bf X}$ be the self-similar growth-fragmentation with extinction time $\epsilon$, let $\alpha$ be its self-similarity parameter, and let $\omega_{+}$ denote the distinguished…

Let $X$ be the self-similar Lévy process considered in the paper, let ${}^q\!M_N^\tau(\omega)$ denote its empirical moment of order $q$ at scale $\tau$, and let $\nu_e(q)$ be the e…

Let $T^{(X)}(t)$ be the clock associated with the self-similar process $X$, let $(\xi_s)_{s\geq 0}$ be the Lévy process appearing in its Lamperti representation, and let $\psi$ be…

Extinction-time scaling conjecture. Theorem should remain true for generic non-geometric self-similar fragmentations with negative index: after rescaling by the appropriate power o…