4 problems

Let $W_\infty^{(x)}$ and $D_\infty^{(x)}$ denote the truncated martingales started from position $x$, and let $\kappa$ be the parameter appearing in the tail behavior of…

Equality of the tail constants. The constants $C_1$ and $C_2$ are equal. This would sharpen the established two-sided asymptotic-order estimate for the tail probability of the whol…

Mean-regime conjecture. There exists a constant $C_{\mathrm{m}}>0$ such that, for every $y\in\mathbb{R}$,

Let $\varrho_{n,n-k}$ denote the point measure of particles at generation $n$ whose most recent common ancestor with the minimum particle is at least $n-k$ generations from the roo…