The concept of equilibrium of a macrosystem (based on the concentration of measure phenomena)

In the talk the basic technique necessary for research of dynamics of macrosystems at large values of time is resulted. In the core of the dynamics lies ergodic markovian chain with huge number of states. At large values of time distribution of macrosystem on macrostates will be close to the stationary. With growth of dimension of a macrosystem (quantity of states of markovian chain) stationary distribution will be concentrate in a small vicinity of the most probable macrostate which is accepted for equilibrium of the given macrosystem. As an example of application of the described formalism, it is resulted to a derivation of static Google’s PageRank model and modernized gravitational model of calculation of a matrix of correspondence from the “reasonable” (individually favorable) dynamics of exchanges of residences. At the end of the talk we plane to describe a general scheme of macrosystem equilibriums investigation. This scheme allows to growth the dimension of the space of macrostates when the number of agents is growth.