5 problems

Finite-reinforcement percolation conjecture. Assume that $d=k=2$. Then there exists $\alpha_0>0$ such that

Percolation conjecture for $d=k=2$. Assume that $d=k=2$. Then

Consider the reinforced $k$-out percolation model on the hypercubic lattice $\mathbb Z^d=(V,E)$, with edge weights initially equal to $1$. At each time step, every vertex selects a…

Let $Z$ be a reinforced Galton–Watson process with reproduction law $\boldsymbol{\nu}$ and reinforcement parameter $q$, and let $m_{\boldsymbol{\nu},q}$ be its mean population grow…

Let $Z=(Z(n))_{n\geq 0}$ be a reinforced Galton–Watson process, and let $Z_*=(Z_*(n))_{n\geq 0}$ be the Galton–Watson subprocess obtained by suppressing every sibling whose size is…