TY - INPR A1 - Pfäffle, Frank A1 - Stephan, Christoph A. T1 - Chiral asymmetry and the spectral action N2 - We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)20 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60046 ER - TY - INPR A1 - Bär, Christian T1 - Renormalized integrals and a path integral formula for the heat kernel on a manifold N2 - We introduce renormalized integrals which generalize conventional measure theoretic integrals. One approximates the integration domain by measure spaces and defines the integral as the limit of integrals over the approximating spaces. This concept is implicitly present in many mathematical contexts such as Cauchy's principal value, the determinant of operators on a Hilbert space and the Fourier transform of an L^p function. We use renormalized integrals to define a path integral on manifolds by approximation via geodesic polygons. The main part of the paper is dedicated to the proof of a path integral formula for the heat kernel of any self-adjoint generalized Laplace operator acting on sections of a vector bundle over a compact Riemannian manifold. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)21 KW - Renormalized integral KW - path integral KW - Feynman-Kac formula KW - generalized Laplace operator KW - Riemannian manifold Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60052 ER - TY - INPR A1 - Bär, Christian T1 - Some properties of solutions to weakly hypoelliptic equations N2 - A linear differential operator L is called weakly hypoelliptic if any local solution u of Lu = 0 is smooth. We allow for systems, i.e. the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which covers all elliptic, overdetermined elliptic, subelliptic and parabolic equations. We extend several classical theorems from complex analysis to solutions of any weakly hypoelliptic equation: the Montel theorem providing convergent subsequences, the Vitali theorem ensuring convergence of a given sequence, and Riemann's first removable singularity theorem. In the case of constant coefficients we show that Liouville's theorem holds, any bounded solution must be constant and any L^p solution must vanish. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)22 KW - Hypoelliptic operators KW - hypoelliptic estimate KW - Montel theorem KW - Vitali theorem KW - Liouville theorem Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60064 ER - TY - GEN A1 - Seiß, Martin A1 - Spahn, Frank T1 - Hydrodynamics of Saturn’s dense rings T2 - Postprints der Universität Potsdam : Postprint Mathematisch Naturwissenschaftliche Reihe N2 - The space missions Voyager and Cassini together with earthbound observations re-vealed a wealth of structures in Saturn’s rings. There are, for example, waves being excited at ring positions which are in orbital resonance with Saturn’s moons. Other structures can be assigned to embedded moons like empty gaps, moon induced wakes or S-shaped propeller features. Further-more, irregular radial structures are observed in the range from 10 meters until kilometers. Here some of these structures will be discussed in the frame of hydrodynamical modeling of Saturn’s dense rings. For this purpose we will characterize the physical properties of the ring particle ensemble by mean field quantities and point to the special behavior of the transport coefficients. We show that unperturbed rings can become unstable and how diffusion acts in the rings. Additionally, the alternative streamline formalism is introduced to describe perturbed regions of dense rings with applications to the wake damping and the dispersion relation of the density waves. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 574 KW - granular gas KW - instabilities KW - hydrodynamics KW - planetary rings Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-413139 SP - 191 EP - 218 ER - TY - GEN A1 - Mickelsson, Jouko A1 - Paycha, Sylvie T1 - The logarithmic residue density of a generalized Laplacian T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We show that the residue density of the logarithm of a generalized Laplacian on a closed manifold defines an invariant polynomial-valued differential form. We express it in terms of a finite sum of residues of classical pseudodifferential symbols. In the case of the square of a Dirac operator, these formulas provide a pedestrian proof of the Atiyah–Singer formula for a pure Dirac operator in four dimensions and for a twisted Dirac operator on a flat space of any dimension. These correspond to special cases of a more general formula by Scott and Zagier. In our approach, which is of perturbative nature, we use either a Campbell–Hausdorff formula derived by Okikiolu or a noncommutative Taylor-type formula. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 649 KW - residue KW - index KW - Dirac operators Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-413680 SN - 1866-8372 IS - 649 ER - TY - INPR A1 - Keller, Peter T1 - Erzeugung gleichverteilter Stichproben von Lozenge-Teilungen mittels Kopplung von Markovketten N2 - Aus dem Inhalt: 1 Einleitung 2 Eigenschaften der Lozengeteilungen 3 Coupling From The Past (CFTP) 4 Simulation von uniform verteilten Lozengeteilungen 5 Programmlisting und Diskussion der Implementierung 6 Ausblick A Anhang T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2009, 02 Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49506 ER - TY - INPR A1 - Zehmisch, René T1 - Über Waldidentitäten der Brownschen Bewegung N2 - Aus dem Inhalt: 1 Abraham Wald (1902-1950) 2 Einführung der Grundbegriffe. Einige technische bekannte Ergebnisse 2.1 Martingal und Doob-Ungleichung 2.2 Brownsche Bewegung und spezielle Martingale 2.3 Gleichgradige Integrierbarkeit von Prozessen 2.4 Gestopptes Martingal 2.5 Optionaler Stoppsatz von Doob 2.6 Lokales Martingal 2.7 Quadratische Variation 2.8 Die Dichte der ersten einseitigen Überschreitungszeit der Brown- schen Bewegung 2.9 Waldidentitäten für die Überschreitungszeiten der Brownschen Bewegung 3 Erste Waldidentität 3.1 Burkholder, Gundy und Davis Ungleichungen der gestoppten Brown- schen Bewegung 3.2 Erste Waldidentität für die Brownsche Bewegung 3.3 Verfeinerungen der ersten Waldidentität 3.4 Stärkere Verfeinerung der ersten Waldidentität für die Brown- schen Bewegung 3.5 Verfeinerung der ersten Waldidentität für spezielle Stoppzeiten der Brownschen Bewegung 3.6 Beispiele für lokale Martingale für die Verfeinerung der ersten Waldidentität 3.7 Überschreitungszeiten der Brownschen Bewegung für nichtlineare Schranken 4 Zweite Waldidentität 4.1 Zweite Waldidentität für die Brownsche Bewegung 4.2 Anwendungen der ersten und zweitenWaldidentität für die Brown- schen Bewegung 5 Dritte Waldidentität 5.1 Dritte Waldidentität für die Brownsche Bewegung 5.2 Verfeinerung der dritten Waldidentität 5.3 Eine wichtige Voraussetzung für die Verfeinerung der drittenWal- didentität 5.4 Verfeinerung der dritten Waldidentität für spezielle Stoppzeiten der Brownschen Bewegung 6 Waldidentitäten im Mehrdimensionalen 6.1 Erste Waldidentität im Mehrdimensionalen 6.2 Zweite Waldidentität im Mehrdimensionalen 6.3 Dritte Waldidentität im Mehrdimensionalen 7 Appendix T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2008, 04 Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49469 ER - TY - INPR A1 - Klein, Markus A1 - Zitt, Pierre-André T1 - Resonances for a diffusion with small noise N2 - We study resonances for the generator of a diffusion with small noise in R(d) : L = -∈∆ + ∇F * ∇, when the potential F grows slowly at infinity (typically as a square root of the norm). The case when F grows fast is well known, and under suitable conditions one can show that there exists a family of exponentially small eigenvalues, related to the wells of F. We show that, for an F with a slow growth, the spectrum is R+, but we can find a family of resonances whose real parts behave as the eigenvalues of the "quick growth" case, and whose imaginary parts are small. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2008, 02 Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49448 ER - TY - INPR A1 - Läuter, Henning T1 - Empirical Minimax Linear Estimates N2 - We give the explicit solution for the minimax linear estimate. For scale dependent models an empirical minimax linear estimates is de¯ned and we prove that these estimates are Stein's estimates. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2008, 06 Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49483 ER - TY - GEN A1 - Mazzonetto, Sara A1 - Salimova, Diyora T1 - Existence, uniqueness, and numerical approximations for stochastic burgers equations T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1393 KW - stochastic Burgers equations KW - SPDEs KW - mild solution KW - existence KW - numerical approximation Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-515796 SN - 1866-8372 IS - 4 ER -