We study the measures on the configuration spaces of particles of two types. Gibbs measures on such spaces are described. Main properties of corresponding relative energy densities and correlation functions are considered. In particular, we show that a support set for such Gibbs measure is the set of pairs of non-intersected configurations.

Індекс рубрикатора НБУВ: В162.13

Рубрики:

Лінійні оператори і лінійні операторні рівняння

Шифр НБУВ: Ж41243 Пошук видання у каталогах НБУВ 

A construction of measures on configuration spaces defined by relative energies is presented. Integral equations for corresponding correlation functionals are studied. Conditions for the existence and uniqueness of measures in terms of the relative energies are found.

Properties of a contact process in continuum for a system of particles of two types, one which is independent of the other, are considered. We study dynamics of the first and the second order correlation functions, their asymptotics, and the dependence on parameters of the system.

We discover death-immigration non-equilibrium stochastic dynamics in the continuum also known as the Surgailis process. Explicit expression for the correlation functions is presented. Dynamics of states and their generating functionals are studied. Ergodic properties for the evolutions are considered.

We construct the time evolution of Kawasaki dynamics for a spatial infinite particle system in terms of generating functionals. This is carried out by an Ovsjannikov-type result in a scale of Banach spaces, which leads to a local (in time) solution. An application of this approach to Vlasov-type scaling in terms of generating functionals is considered as well.

We consider Vlasov-type scaling for Markov evolution of birth-and-death type in continuum, which is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. The existence of rescaled and limiting evolutions of correlation functions and convergence to the limiting evolution are shown. The obtained results enable us to derive a non-linear Vlasov-type equation for the density of the limiting system.

Індекс рубрикатора НБУВ: В162.13

Рубрики:

Лінійні оператори і лінійні операторні рівняння

Шифр НБУВ: Ж41243 Пошук видання у каталогах НБУВ 

Здійснено стислий огляд відомих фактів про простори дискретних мір Радона, які можуть розглядатися як узагальнення просторів конфігурацій. Розглянуто три марківські динаміки на просторах дискретних мір Радона: аналоги моделі контактів та моделі Болкера - Дікмана - Лоу - Пакали та аналог динаміки типу Глаубера. Показано як результати, одержані для просторів конфігурацій, можуть бути узагальнені для випадки просторів дискретних мір Радона.