Piotr Brzeski

Percolation of hyperspheres in dimensions 3 to 5

In my talk I will present a method of studying the onset of percolation of overlapping discrete hyperspheres on hypercubic lattices in dimension D = 3, 4, 5. Taking the continuum limit of the thresholds for discrete hyperspheres we obtain the values of percolation thresholds for continuous hyperspheres. In D = 3 we improved the value of the correlation length exponent. In D = 4 and 5 we obtained the continuous percolation thresholds of hyperspheres with much better quality than previously known.