A proof of the Bunkbed conjecture on the complete graph for p\geqslant1/2

2018/02/13 by Paul de Buyer, de Buyer, Paul
Mathematics · #60K35 #82B43 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1802.04694

openalex publication_date 2018/02/13 · openalex created_date 2018/02/23 · openalex updated_date 2026/07/28

Abstract

The bunkbed of a graph G is the graph G×\ 0,1\ . It has been conjectured that in the independent bond percolation model, the probability for (u,0) to be connected with (v,0) is greater than the probability for (u,0) to be connected with (v,1), for any vertex u, v of G. In this article, we prove this conjecture for the complete graph in the case of the independent bond percolation of parameter p\geqslant1/2.

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