Given an invariant bond percolation on the d-regular tree, where the probability of an edge to be open equals p, is it always possible to find, with positive probability, an infinite self-avoiding path along which the density of open edges is bigger than p? We give positive answer when d ≥ 4 and explore related questions.
|Original language||American English|
|Title of host publication||Contemporary Mathematics|
|Publisher||American Mathematical Society|
|State||Published - 2018|
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©2018 Amerian Mathematial Soiety.