2 citations · 3 across the 4 of their papers we have counts for
4 papers
invariant random subsets of
Mikołaj Frączyk, Simon Machado
We classify measures on , , the space of subsets of , which are invariant under all affine special linear transformations. In other…
Benjamini--Schramm convergence of arithmetic locally symmetric spaces
Mikołaj Frączyk, Sebastian Hurtado, Jean Raimbault
We prove that the thin parts of arithmetically defined locally symmetric space take up a negligible part of their volume and deduce asymptotic results on their Betti numbers.
Growth dichotomy for unimodular random rooted trees
Miklós Abert, Mikołaj Frączyk, Ben Hayes
We show that the growth of a unimodular random rooted tree of degree bounded by always exists, assuming its upper growth passes the critical threshold . Thi…
Betti numbers of Shimura curves and arithmetic three--orbifolds
Mikołaj Frączyk, Jean Raimbault
We show that asymptotically the first Betti number, or the arithmetic genus, of a Shimura curve satisfies the Gauss--Bonnet equality. We also show that the first Betti number of a…