Page 181 - Special Topic Session (STS) - Volume 4

STS579 Daria Balashova
exceed the number of branching sources with positive intensity, the maximum
of these eigenvalues is simple.
In addition, we can calculate critical values for the intensity of sources,

depending on which process will be subcritical, critical or supercritical:

Consider on ℤ with 3 sources: (1,0,0), (0,1,0) and (0,0,1).
3
We find the values = 1.514 and := ((1, 0, 0), (0, 1, 0)) =... = ((0,
̃
0
0
0
0
1,0),(0,0,1)) = 0.328. Let is a smaller positive root of the equation

for

and for

the are supercritical.
Consider on ℤ with 4 sources: (1,0,0,0), (0,1,0,0), (0,0,1,0) and (0,0,0,1).
4
We find the values = 1.234 and := ((1, 0, 0, 0), (0, 1, 0, 0)) =... =
̃
0
0
0
((0, 0, 1, 0), (0, 0, 0, 1)) = 0.102.
0
The is supercritical for

and for

The research was supported by the , project no. 17-01-00468.

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