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In this paper, a rigorous mathematical analysis of the Krasnoshchekov model is presented. We have shown that in case a community does not contain any group of people having zero resistance to interpersonal influence, which are moreover isolated from the pressure of the rest of community, the Krasnoshchekov opinion readjustment procedure can be reduced to the Friedkin-Johnsen dynamics. In turn, if one repeats the Krasnoshchekov opinion updating rule, the corresponding dynamics forces individuals' opinions to converge eventually to some terminal opinions, which are a consensus under the same conditions as in the French-Harary-DeGroot dynamics. Otherwise, the Krasnoshchekov dynamics exhibits patterns, which are much closer to the behavior of electrons in the superconductivity state. [ABSTRACT FROM AUTHOR]

Holland and Leinhardt {1977a) introduced a continuous time Markov chain to model changes in a social network. Their model was further studied by Wasserman (1977) . Holland and Leinhardt (1977b) have also proposed a general class of probability measures on random networks, The purpose of this paper is to show that these probability measures may be viewed as Gibbs measures induced by a nearest neighbor potential. As such they have a Markov field property which is a natural generalization of Markov chains to spatial situations, The dynamic models are shown to fit into a general, class of Markov processes suggested by the study of interacting particle systems. A related "voter model" is discussed. [ABSTRACT FROM AUTHOR]