Abstract
This thesis is an investigation of some aspects of inhomogeneous Bernoulli bond percolation in two different graphs.
First, we show the continuity of the critical curve in the qpplane for inhomogeneous Bernoulli bond percolation on ladder graphs. We prove that such property can be achieved even if the graph possesses infinitely many columnar inhomogeneities, provided that they are not too close from each other.
Second, we study the model of inhomogeneous Bernoulli bond percolation on the ordinary ddimensional hypercubic lattice, d higher than 3, with an sdimensional sublattice of defects, s smaller than d. In this model, every edge inside the sdimensional sublattice is open with probability q and every other edge is open with probability p. We prove two results: first, the uniqueness of the infinite cluster in the supercritical phase of parameters (p,q), whenever p is different from the threshold for homogeneous percolation; second, we show that, for any p smaller than this threshold, the critical points in the pqplane can be approximated by critical points of slabs, in the spirit of the classical theorem of Grimmett and Marstrand for homogeneous percolation.
First, we show the continuity of the critical curve in the qpplane for inhomogeneous Bernoulli bond percolation on ladder graphs. We prove that such property can be achieved even if the graph possesses infinitely many columnar inhomogeneities, provided that they are not too close from each other.
Second, we study the model of inhomogeneous Bernoulli bond percolation on the ordinary ddimensional hypercubic lattice, d higher than 3, with an sdimensional sublattice of defects, s smaller than d. In this model, every edge inside the sdimensional sublattice is open with probability q and every other edge is open with probability p. We prove two results: first, the uniqueness of the infinite cluster in the supercritical phase of parameters (p,q), whenever p is different from the threshold for homogeneous percolation; second, we show that, for any p smaller than this threshold, the critical points in the pqplane can be approximated by critical points of slabs, in the spirit of the classical theorem of Grimmett and Marstrand for homogeneous percolation.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  22Dec2020 
Place of Publication  [Groningen] 
Publisher  
DOIs  
Publication status  Published  2020 