Laboratory of Structural Methods of Data Analysis in Predictive
Modeling Moscow Institute of Physics and Technology
About possible dynamic in PageRank model and modernized model of correspondence matrix calculation
In this paper, the basic technique for research of macrosystems dynamics at large time
values is developed. In the core of the dynamics lies the ergodic markovian chain with a huge
number of states. At large time values the macrosystem distribution over macrostates is close
to a stationary one. With growth of macrosystem dimension (the number of markovian chain
states), the stationary distribution is concentrated in a small vicinity of the most probable
macrostate accepted for the given macrosystem equilibrium. As an example of application
of the described formalism, we give the derivation of the static Google’s PageRank model
and the modernized gravitational model for calculating a correspondence matrix from the
?reasonable? (individually favorable) dynamics of residences exchanges. At the end of
the paper we describe the general scheme of macrosystem equilibriums investigation. This
scheme allows us to increase the dimension of macrostates space when the number of agents

Авторы: Gasnikov Alexander , Gasnikova, EV

Дата: 16 ноября 2014

Статус: опубликована

Журнал: Trudy MIPT

Том: 4

Выпуск: 2

Страницы: 101-120

Год: 2012

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