Thomas Richthammer

activity

20042022

most citedProof of Aldous' spectral gap conjecture

74 citations · 117 across the 12 of their papers we have counts for

collaborators

13 papers

math.PR2022★ 1 cited

Monotonicity properties for Bernoulli percolation on layered graphs -- a Markov chain approach

Philipp König, Thomas Richthammer

A layered graph $G^{\times}$ is the Cartesian product of a graph $G = (V, E)$ with the linear graph $Z$ , e.g. $Z^{\times}$ is the 2D square lattice $Z^{2}$ . For Bernoulli percolation with…

math.PR2022

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

Philipp König, 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.PR2022★ 5 cited

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.PR2022★ 1 cited

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…

math-ph2019

A lower bound on the displacement of particles in 2D Gibbsian particle systems

Michael Fiedler, Thomas Richthammer

While 2D Gibbsian particle systems might exhibit orientational order resulting in a lattice-like structure, these particle systems do not exhibit positional order if the interactio…

math-ph2015★ 6 cited

Lower bound on the mean square displacement of particles in the hard disk model

Thomas Richthammer

The hard disk model is a 2D Gibbsian process of particles interacting via pure hard core repulsion. At high particle density the model is believed to show orientational order, howe…

Monotonicity properties for Bernoulli percolation on layered graphs -- a Markov chain approach

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)

A lower bound on the displacement of particles in 2D Gibbsian particle systems

Lower bound on the mean square displacement of particles in the hard disk model

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