Browsing by Author "Kuna, Tobias"
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- Analytic aspects of Poissonian white noise analysisPublication . Kondratiev, Yuri G.; Kuna, Tobias; Oliveira, Maria JoãoGeneral structures of Poissonian white noise analysis are presented.Simultaneously, the theory is developed on Poisson and Lebesgue- Poisson space. Both spaces have an own S-transform, well known in the Gaussian case. They give an extra connection between these two spaces via the Bargmann-Segal space. Test and generalized functions,different types of convolutions, and representations of creation and annihilation operators in the aforementioned spaces are considered.
- Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spacesPublication . Kondratiev, Yuri G.; Kuna, Tobias; Oliveira, Maria JoãoHarmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L2-spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expansion. This permits,in particular, to derive an explicit expression for the generator of the second quantization of a sub-Markovian contraction semigroup on a set of functions which forms a core of the generator.
- 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.
- Results about the free kawasaki dynamics of continuous particle systems in infinite volume: long-time asymptotics and hydrodynamic limitPublication . Kondratiev, Yuri G.; Kuna, Tobias; Oliveira, Maria João; Silva, José Luís da; Streit, LudwigAn infinite particle system of independent jumping particles in infinite volume is considered. Their construction is recalled, further properties are derived, the relation with hierarchical equations, Poissonian analysis, and second quantization are discussed. The hydrodynamic limit for a general initial distribution satisfying a mixing condition is derived. The long-time asymptotics is computed under an extra assumption. The relation with constructions based on infinite volume limits is discussed.
- Stochastic and infinite dimensional analysisPublication . Bernido, Christopher C.; Carpio-Bernido, Maria Victoria; Grothaus, Martin; Kuna, Tobias; Oliveira, Maria João; Silva, José Luís daThis volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.