Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  study percolation on finite Cayley graphs. A conjecture of Benjamini says that the critical percolation $p_c$ of any vertex-transitive graph satisfying a certain diameter condition can be bounded away from one.  prove Benjamini's conjecture for some special classes of Cayley graphs.  also establish a reduction theorem, which allows us to build Cayley graphs for large groups without increasing $p_c$.
['Christopher Malon', 'Igor Pak']
I am writing a research paper on a idea Percolation on Finite Cayley Graphs
[{"from": "human", "value": "I am writing a research paper on a idea Percolation on Finite Cayley Graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  study percolation on finite Cayley graphs. A conjecture of Benjamini says that the critical percolation $p_c$ of any vertex-transitive graph satisfying a certain diameter condition can be bounded away from one.  prove Benjamini's conjecture for some special classes of Cayley graphs.  also establish a reduction theorem, which allows us to build Cayley graphs for large groups without increasing $p_c$."}]