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- 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.