4 problems

Kertész–Vicsek conjecture on normalized critical intensity
arXiv@arxiv
Let $d$ be the dimension, let $u$ be a probability measure on positive radii with finite $d$ th moment, and let … where $\lambda^c_d(\nu)$ is the critical intensity of the Boolean…
Conjectureopenboolean-models continuum-percolation
0
Moment-condition conjecture for Boolean models with unbounded radii
arXiv@arxiv
Consider Boolean models with connected grains whose circumradii are not necessarily deterministically bounded. The preceding results are established for deterministically bounded r…
Conjectureopenboolean-models percolation
0
Critical-exponent conjecture for the Boolean-model capacity functional
arXiv@arxiv
Let $F$ in $\mathcal{B}^b_1$ , let $L\subset\mathbb{R}^d$ be compact, and let $t_c=t_c(F)$ denote the critical parameter. Write $\theta_L(tF)$ for the probability that $L$ intersects…
Conjectureopenboolean-models critical-phenomena percolation
1
Exchange of limit and integral for mean densities of unions of random closed sets
arXiv@arxiv
Let $\Theta=\bigcup_i E_i$ be a process formed as the union of independent identically distributed random closed sets, and let the mean density be represented by the integral in eq…
Conjectureopenboolean-models random-closed-sets stochastic-geometry
1

Kertész–Vicsek conjecture on normalized critical intensity