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- Markov evolutions and hierarchical equations in the continuum. I: one-component systemsPublication . Finkelshtein, Dmitri L.; Kondratiev, Yuri G.; Oliveira, Maria JoãoGeneral birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General considerations are illustrated in a number of concrete examples of Markov evolutions appearing in applications.
- Glauber dynamics in the continuum via generating functionals evolutionPublication . Finkelshtein, Dmitri L.; Kondratiev, Yuri G.; Oliveira, Maria JoãoWe construct the time evolution for states of Glauber 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, leading to a local (in time) solution which, under certain initial conditions, might be extended to a global one. An application of this approach to Vlasov-type scaling in terms of generating functionals is considered as well.
- Markov evolutions and hierarchical equations in the continuum. II: multicomponent systemsPublication . Finkelshtein, Dmitri L.; Kondratiev, Yuri G.; Oliveira, Maria JoãoGeneral birth-and-death as well as hopping stochastic dynamics of infinite multicomponent particle systems in the continuum are considered. We derive the corresponding evolution equations for quasi-observables and correlation functions. We also present sufficient conditions that allow us to consider these equations on suitable Banach spaces.
- Kawasaki dynamics in the continuum via generating functionals evolutionPublication . Finkelshtein, Dmitri L.; Kondratiev, Yuri G.; Oliveira, Maria JoãoWe 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.
- Holomorphic Bogoliubov functionals for interacting particle systems in continuumPublication . Kondratiev, Yuri G.; Kuna, Tobias; Oliveira, Maria JoãoCombinatorial harmonic analysis techniques are used to develop new analytical methods for the study of interacting particle systems in continuum based on a Bogoliubov functional approach. Concrete applications of the methods are presented, namely, conditions for the existence of Bogoliubov functionals, a uniqueness result for Gibbs measures in the high temperature regime. We also propose a new approach to the study of non-equilibrium stochastic dynamics in terms of evolution equations for Bogoliubov functionals.
- On the relations between Poissonian white noise analysis and harmonic analysis on configuration spacesPublication . Kondratiev, Yuri G.; Kuna, Tobias; Oliveira, Maria JoãoWe unify techniques of Poissonian white noise analysis and harmonic analysis on configuration spaces establishing relations between the main structures of both ones. This leads to new results inside of infinite-dimensional analysis as well as in its applications to problems of mathematical physics, e.g., statistical mechanics of continuous systems.