Let μ (F) be the time constant of first-passage percolation on the square lattice with underlying distribution function F. Two theorems are presented which show, under some restrictions, that μ varies ...

Percolation theory examines the emergence of connected clusters in systems composed of randomly occupied sites or bonds, making it an invaluable framework for understanding phase transitions in ...

The star—triangle transformation is used to obtain an equivalence extending over the set of all (in)homogeneous bond percolation models on the square, triangular and hexagonal lattices. Among the ...