Limiting theorems in statistical mechanics. The mean-field case.

The Curie-Weiss model is defined by ah Hamiltonian according to spins interact. For some particular values of the parameters, the sum of the spins normalized with square-root normalization converges or not toward Gaussian distribution. In the thesis we investigate some correlations between the behaviour of the sum and the central limit for interacting random variables.

Herbrand Theorems for Substructural Logics

Herbrand and Skolemization theorems are obtained for a broad family of first-order substructural logics. These logics typically lack equivalent prenex forms, a deduction theorem, and reductions of semantic consequence to satisfiability. The Herbrand and Skolemization theorems therefore take various forms, applying either to the left or right of the consequence relation, and to restricted classes of formulas.

Limit theorems for nondegenerate U-statistics of continuous semimartingales

This paper presents the asymptotic theory for nondegenerate U-statistics of high frequency observations of continuous Itô semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.

Multifractional Poisson process, multistable subordinator and related limit theorems

We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and establish the convergence of a continuous-time random walk to the multifractional Poisson process.

Petition der Berliner Katzen-Musikanten: Allerdurchlauchtigster, Großmächtigster, Allergnädigster König der Sandwich-Inseln! Wir, die unterzeichneten constitutionellen Katzenmusikanten von Berlin, nahen uns voll Ehrfurcht Deinem erhabenen Throne ...

Welsch (Projektbearbeiter): Satirische Rechtfertigung der Katzenmusiken (Charivaris) in der Form einer persiflierten Petition an den als 'König der Sandwich-Inseln' titulierten Friedrich Wilhelm IV.

Darstellung der Lebens-Art der Sandwich-Insulaner

[hrsg. durch] J. A. Riemer