{"publication":"Stochastic Processes and their Applications","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"A layered graph G^× is the Cartesian product of a graph G = (V, E) with the linear graph Z, e.g. Z^× is the 2D square lattice Z^2. For Bernoulli percolation with parameter p ∈ [0, 1] on G^× one intuitively would expect that P_p((o, 0) ↔ (v, n)) ≥ P_p((o, 0) ↔ (v, n + 1)) for all o, v ∈ V and n ≥ 0. This is reminiscent of the better known bunkbed conjecture. Here\r\nwe introduce an approach to the above monotonicity conjecture that makes use of a Markov chain building the percolation pattern layer by layer. In case of finite G we thus can show that for some N ≥ 0 the above holds\r\nfor all n ≥ N o, v ∈ V and p ∈ [0, 1]. One might hope that this Markov chain approach could be useful for other problems concerning Bernoulli percolation on layered graphs"}],"user_id":"62054","_id":"64213","language":[{"iso":"eng"}],"article_number":"104549","publication_identifier":{"issn":["0304-4149"]},"publication_status":"published","intvolume":"       181","citation":{"ama":"König P, Richthammer T. Monotonicity properties for Bernoulli percolation on layered graphs— A Markov chain approach. <i>Stochastic Processes and their Applications</i>. 2024;181. doi:<a href=\"https://doi.org/10.1016/j.spa.2024.104549\">10.1016/j.spa.2024.104549</a>","chicago":"König, Philipp, and Thomas Richthammer. “Monotonicity Properties for Bernoulli Percolation on Layered Graphs— A Markov Chain Approach.” <i>Stochastic Processes and Their Applications</i> 181 (2024). <a href=\"https://doi.org/10.1016/j.spa.2024.104549\">https://doi.org/10.1016/j.spa.2024.104549</a>.","ieee":"P. König and T. Richthammer, “Monotonicity properties for Bernoulli percolation on layered graphs— A Markov chain approach,” <i>Stochastic Processes and their Applications</i>, vol. 181, Art. no. 104549, 2024, doi: <a href=\"https://doi.org/10.1016/j.spa.2024.104549\">10.1016/j.spa.2024.104549</a>.","bibtex":"@article{König_Richthammer_2024, title={Monotonicity properties for Bernoulli percolation on layered graphs— A Markov chain approach}, volume={181}, DOI={<a href=\"https://doi.org/10.1016/j.spa.2024.104549\">10.1016/j.spa.2024.104549</a>}, number={104549}, journal={Stochastic Processes and their Applications}, publisher={Elsevier BV}, author={König, Philipp and Richthammer, Thomas}, year={2024} }","short":"P. König, T. Richthammer, Stochastic Processes and Their Applications 181 (2024).","mla":"König, Philipp, and Thomas Richthammer. “Monotonicity Properties for Bernoulli Percolation on Layered Graphs— A Markov Chain Approach.” <i>Stochastic Processes and Their Applications</i>, vol. 181, 104549, Elsevier BV, 2024, doi:<a href=\"https://doi.org/10.1016/j.spa.2024.104549\">10.1016/j.spa.2024.104549</a>.","apa":"König, P., &#38; Richthammer, T. (2024). Monotonicity properties for Bernoulli percolation on layered graphs— A Markov chain approach. <i>Stochastic Processes and Their Applications</i>, <i>181</i>, Article 104549. <a href=\"https://doi.org/10.1016/j.spa.2024.104549\">https://doi.org/10.1016/j.spa.2024.104549</a>"},"year":"2024","volume":181,"date_created":"2026-02-18T12:06:28Z","author":[{"first_name":"Philipp","full_name":"König, Philipp","last_name":"König"},{"first_name":"Thomas","full_name":"Richthammer, Thomas","id":"62054","last_name":"Richthammer"}],"publisher":"Elsevier BV","date_updated":"2026-02-18T12:32:13Z","doi":"10.1016/j.spa.2024.104549","title":"Monotonicity properties for Bernoulli percolation on layered graphs— A Markov chain approach"}