4 problems

Limit theorem for negative critical $(k+1)$-face processes. The same limit theorem as the one established for the positive critical $k$-face process and the restricted negative cri…

Let $d\geq 2$ and $1\leq k\leq d-1$ be fixed. Let $\Pi_k(n)$ denote the maximal multiplicative persistence over all $k$-cycles in the persistent homology of a random Vietoris–Rips…

Let $\mathcal{M}$ be an $m$-dimensional manifold, let $\hat\beta_i(n,r)=\beta_i(n,r)-\beta_i(\mathcal{M})$ denote the noisy $i$-th Betti number, and define … The radii $\rho_i$ and…

Let $\mathcal{C}(n,r)$ be the random geometric complex and let $\beta_i(n,r)$ denote its $i$-th Betti number. Consider the curves of the different Betti numbers as the radius $r$ v…