Nonergodicity of Uniform Threshold Networks for Small Self-Excitation

The article considers the behavior of networks composed of elements which are capable of spontaneous excitation. It is shown that the network is nonergodic for small self-excitation probabilities if and only if the inequality $p\geq\frac{N}{2}+1$ holds, where $p$ is the threshold and $N$ is the number of inputs for a network element.