7 papers · 1 filter
Detection of first homology via random geometric graphs in the thermodynamic regime
Christian Gorski
Consider a random geometric graph on a compact Riemannian manifold , whose vertices are a cloud of independently sampled points, and whose edges connect vertices…
The geometry of the giant component of random geometric graphs
Karoline Dubin, Christian Gorski, Marcus Michelen
Consider a random geometric graph whose vertex set consists of points chosen independently and uniformly from a Riemannian manifold , with edges joining pairs of…
Lipschitz continuity of the time constant for continuum percolation
Karoline Dubin, Christian Gorski
We consider the Boolean model of continuum percolation, where points are placed in by a Poisson point process and pairs of points with distance at most 1 are connect…
The CLT for lamplighter groups with an acylindrically hyperbolic base
Maksym Chaudkhari, Christian Gorski, Eduardo Silva
We prove a Central Limit Theorem for the drift of a non-elementary random walk with a finite exponential moment on a wreath product with a non…
Chemical distance in graphs of polynomial growth
Christian Gorski, Eviatar B. Procaccia
We prove an Antal-Pisztora type theorem for transitive graphs of polynomial growth. That is, we show that if is a transitive graph of polynomial growth and , then f…
Strict monotonicity for first passage percolation on graphs of polynomial growth and quasi-trees
Christian Gorski
In 1993 van den Berg and Kesten proved a strict monotonicity theorem for first passage percolation on , : given two probability measures and wi…
Asymptotic shapes for stationary first passage percolation on virtually nilpotent groups
Antonio Auffinger, Christian Gorski
We study first passage percolation (FPP) with stationary edge weights on Cayley graphs of finitely generated virtually nilpotent groups. Previous works of Benjamini-Tessera and Can…