preprint Thomas Richthammer author 62054 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 V_+ and in the set V_-, where V_+,V_- \subset V have the same size. Intuitively, if V_- is further away from o than V_+, it should contain fewer vertices of the cluster. We prove such a result in terms of stochastic domination, provided that o \in V_+, and V_+,V_- satisfy some strong symmetry conditions, and we give applications of this result in case G is a bunkbed graph, a layered graph, the 2D square lattice or a hypercube graph. Our result only relies on general probabilistic techniques and a combinatorial result on group actions, and thus extends to fairly general random partitions, e.g. as induced by Bernoulli site percolation or the random cluster model. 2022 eng @article{Richthammer_2022, title={Comparing the number of infected vertices in two symmetric sets for Bernoulli percolation (and other random partitions)}, author={Richthammer, Thomas}, year={2022} } Richthammer T. Comparing the number of infected vertices in two symmetric sets for Bernoulli percolation (and other random partitions). Published online 2022. T. Richthammer, (2022). Richthammer, Thomas. “Comparing the Number of Infected Vertices in Two Symmetric Sets for Bernoulli Percolation (and Other Random Partitions),” 2022. T. Richthammer, “Comparing the number of infected vertices in two symmetric sets for Bernoulli percolation (and other random partitions).” 2022. Richthammer, Thomas. <i>Comparing the Number of Infected Vertices in Two Symmetric Sets for Bernoulli Percolation (and Other Random Partitions)</i>. 2022. Richthammer, T. (2022). <i>Comparing the number of infected vertices in two symmetric sets for Bernoulli percolation (and other random partitions)</i>. 642142026-02-18T12:13:09Z2026-02-18T12:13:21Z