3 problems
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Recurrence and transience criteria for weight-dependent random connection models
Let , let be a kernel satisfying … and let be a profile function satisfying the source's condition for some . Define … Assume that … Let…
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The transient-boundary conjecture for the two-dimensional weight-dependent random connection model
For , let be the profile function and let and be the parameters represented by the phase diagram in part (b). The transient regime is the region in whi…
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The conjecture that isotropy is not essential in random connection models
The random connection model uses a connection function and commonly assumes that is isotropic; that is, the connection probability depends only on the distance between node…