Thomas Richthammer

collaborators

3 papers

math.PR2025

Monotonicity of Markov chain transition probabilities via quasi-stationarity -- an application to Bernoulli percolation on $C_{k} \times Z$

Philipp KÃ¶nig, Thomas Richthammer

Let $X_{n}, n \geq 0$ be a Markov chain with finite state space $M$ . If $x, y \in M$ such that $x$ is transient we have $P^{y} (X_{n} = x) \to 0$ for $n \to \infty$ , and under mild aperiodi…

math.PR2025

Bunkbed conjecture for complete bipartite graphs and related classes of graphs

Thomas Richthammer

Let $G = (V, E)$ be a simple finite graph. The corresponding bunkbed graph $G^{\pm}$ consists of two copies $G^{+} = (V^{+}, E^{+}), G^{-} = (V^{-}, E^{-})$ of $G$ and additional edges connecting an…

math.PR2025

Comparing the number of infected vertices in two symmetric sets for Bernoulli percolation (and other random partitions)

Thomas Richthammer

For Bernoulli percolation on a given graph $G = (V, E)$ we consider the cluster of some fixed vertex $o \in V$ . We aim at comparing the number of vertices of this cluster in the set…

Monotonicity of Markov chain transition probabilities via quasi-stationarity -- an application to Bernoulli percolation on Ck​×Z

Bunkbed conjecture for complete bipartite graphs and related classes of graphs

Comparing the number of infected vertices in two symmetric sets for Bernoulli percolation (and other random partitions)

Monotonicity of Markov chain transition probabilities via quasi-stationarity -- an application to Bernoulli percolation on $C_{k} \times Z$