Abstract:
Percolation models in which defect centers are distributed randomly in space in
accordance with Poisson's law and the shape of each defect is also random are
considered. Coincidence of two critical points is proved. One of these corresponds
to the time when the mean number of defects connected to a given defect
becomes infinite. The other corresponds to the existence of percolation in an
arbitrarily large region of space.
Citation:
S. A. Zuev, A. F. Sidorenko, “Continuous models of percolation theory. I”, TMF, 62:1 (1985), 76–86; Theoret. and Math. Phys., 62:1 (1985), 51–58
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M. V. Menshikov, A. F. Sidorenko, “Coincidence of Critical Points in Poisson Percolation Models”, Theory Probab. Appl., 32:3 (1987), 547–550
S. A. Zuev, A. F. Sidorenko, “Continuous models of percolation theory. II”, Theoret. and Math. Phys., 62:2 (1985), 171–177
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