  Neutrons in a nuclear reactor move along trajectories corresponding to Cayley
trees associated with branching random processes. The probability of
percolation, the appearance of such a state of the Bethe lattice in which there
is at least one continuous path through neighboring conducting nodes through
the entire lattice, corresponds to the probability of the occurrence of a
self-sustaining fission chain reaction. At a critical value of the last
probability, a (conditionally) infinite cluster of neutrons appears. The
probability of percolation, depending on the operating time of the reactor and
its size, is associated with the criticality of the reactor. The temporal
behavior of the neutron multiplication factor is estimated. Particular
attention is paid to the early stages of the development of a self-sustaining
chain reaction of nuclear fission. The possibilities of determining the
boundaries of the critical region are indicated.
