On the monotonicity of the critical time in the Constrained-degree percolation model

Abstract

The Constrained-degree percolation model was introduced in [B.N.B. de Lima, R. Sanchis, D.C. dos Santos, V. Sidoravicius, and R. Teodoro, Stoch. Process. Appl. ( 2020)], where it was proven that this model has a non-trivial phase transition on a square lattice. We study the Constrained-degree percolation model on the d-dimensional hypercubic lattice (Z d ) and, via numerical simulations, found evidence that the critical time t d c (k) is monotonous not increasing in the constrained k if d = 3, 4, like it is when d = 2. We verify that the lowest constrained value k such that the system exhibits a phase transition is k = 3 and that the correlation critical exponent ν for the Constrained-degree percolation model and ordinary Bernoulli percolation are the same.