8 problems

Expected-length phase-transition conjecture. If the limit distribution lies in

Vanishing-kernel conjecture. If $\frak{b}=+$ and $f(R_c)=+$, then

Infinite-condensation-root conjecture. If $\frak{b}=+$ and $f(R_c)=+$, then $\tau_n$ converges locally in distribution towards a limit \tau^ whose root has an infinite number of…

Continuity-at-infinity conjecture. If $R_c>1$, then $\tau^\theta$ converges locally in distribution towards \tau^ as $\theta\to+$.

High-regime convergence conjecture. If $R_c>1$, equivalently if $W$ has some positive exponential moments, then $\tau_n$ converges locally in distribution towards \tau^ in the hi…

Persistence conjecture. The extra branching remains negligible for a few generations, corresponding roughly to the second term in the definition of $\gamma(\varepsilon)$, and after…

Let $B$ be a random variable with ${\mathbf E}B=1$ and $0<\operatorname{Var}(B)<\infty$. For $n\geq 1$, let $T_n$ be a Galton–Watson tree with offspring distribution $B$, condition…

Distribution conjecture. The pair $({\rm Sch}_\infty,\Delta h)$ is distributed as a Galton–Watson tree with geometric-$1/2$ offspring distribution, conditioned to be infinite, with…