@misc{ImkellerRoelly2007,
  author    = {Imkeller, Peter and Roelly, Sylvie},
  title     = {Die Wiederentdeckung eines Mathematikers: Wolfgang D{\"o}blin},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-16397},
  year      = {2007},
  abstract  = {"Considerons une particule mobile se mouvant aleatoirement sur la droite (ou sur un segment de droite). Supposons qu'il existe une probabilite F(x,y;s,t) bien definie pour que la particule se trouvant a l'instant s dans la position x se trouve a l'instant t (> s) a gauche de y, probabilite independante du mouvement anterieur de la particule...." Mit diesen Worten beginnt eines der ber{\"u}hmtesten mathematischen Manuskripte des letzten Jahrhunderts. Es stammt vom Soldaten Wolfgang D{\"o}blin, Sohn des deutschen Schriftstellers Alfred D{\"o}blin, und tr{\"a}gt den Titel "Sur l'equation de Kolmogoroff". Seine Ver{\"o}ffentlichung verbindet sich mit einer unglaublichen Geschichte. Wolfgang D{\"o}blin, stationiert mit seiner Einheit in den Ardennen im Winter 1939/1940, arbeitete an diesem Manuskript. Er entschloss sich, es als versiegeltes Manuskript an die Academie des Sciences in Paris zu schicken. Aber er kehrte nie aus diesem Krieg zur{\"u}ck. Sein Manuskript blieb 60 Jahre unter Verschluss im Archiv, und wurde erst im Jahre 2000 ge{\"o}ffnet. Wie weit D{\"o}blin damit seiner Zeit voraus war, wurde erkannt, nachdem es von Bernard Bru und Marc Yor ausgewertet worden war. Im ersten Satz umschreibt W. D{\"o}blin gleichzeitig das Programm des Manuskripts: "Wir betrachten ein bewegliches Teilchen, das sich zuf{\"a}llig auf der Geraden (oder einem Teil davon) bewegt." Er widmet sich damit der Aufgabe, die Fundamente eines Gebiets zu legen, das wir heute als stochastische Analysis bezeichnen.},
  language  = {de}
}
@misc{GoychukKharchenko2013,
  author    = {Goychuk, Igor and Kharchenko, Vasyl O.},
  title     = {Rocking subdiffusive ratchets},
  series = {Mathematical Modelling of Natural Phenomena},
  journal   = {Mathematical Modelling of Natural Phenomena},
  number    = {622},
  issn      = {1866-8372},
  doi       = {10.1051/mmnp/20138210},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416138},
  pages     = {15},
  year      = {2013},
  abstract  = {We study origin, parameter optimization, and thermodynamic efficiency of isothermal rocking ratchets based on fractional subdiffusion within a generalized non-Markovian Langevin equation approach. A corresponding multi-dimensional Markovian embedding dynamics is realized using a set of auxiliary Brownian particles elastically coupled to the central Brownian particle (see video on the journal web site). We show that anomalous subdiffusive transport emerges due to an interplay of nonlinear response and viscoelastic effects for fractional Brownian motion in periodic potentials with broken space-inversion symmetry and driven by a time-periodic field. The anomalous transport becomes optimal for a subthreshold driving when the driving period matches a characteristic time scale of interwell transitions. It can also be optimized by varying temperature, amplitude of periodic potential and driving strength. The useful work done against a load shows a parabolic dependence on the load strength. It grows sublinearly with time and the corresponding thermodynamic efficiency decays algebraically in time because the energy supplied by the driving field scales with time linearly. However, it compares well with the efficiency of normal diffusion rocking ratchets on an appreciably long time scale.},
  language  = {en}
}
@misc{GinouxHabib2008,
  author    = {Ginoux, Nicolas and Habib, Georges},
  title     = {Geometric aspects of transversal Killing spinors on Riemannian flows},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {867},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43478},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-434783},
  pages     = {69 -- 90},
  year      = {2008},
  abstract  = {We study a Killing spinor type equation on spin Riemannian flows. We prove integrability conditions and partially classify those flows carrying non-trivial solutions.},
  language  = {en}
}
@misc{Ginoux2004,
  author    = {Ginoux, Nicolas},
  title     = {Dirac operators on Lagrangian submanifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-5627},
  year      = {2004},
  abstract  = {We study a natural Dirac operator on a Lagrangian submanifold of a K{\"a}hler manifold. We first show that its square coincides with the Hodge - de Rham Laplacian provided the complex structure identifies the Spin structures of the tangent and normal bundles of the submanifold. We then give extrinsic estimates for the eigenvalues of that operator and discuss some examples.},
  language  = {en}
}
@misc{Ginoux2003,
  author    = {Ginoux, Nicolas},
  title     = {Remarques sur le spectre de l'op{\´e}rateur de Dirac},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-5630},
  year      = {2003},
  abstract  = {Nous d{\´e}crivons un nouvelle famille d'exemples d'hypersurfaces de la sph{\`e}re satisfaisant le cas d'{\´e}galit{\´e} de la majoration extrins{\`e}que de C. B{\"a}r de la plus petite valeur propre de l'op{\´e}rateur de Dirac.},
  language  = {fr}
}
@misc{Ginoux2003,
  author    = {Ginoux, Nicolas},
  title     = {Une nouvelle estimation extrins{\`e}que du spectre de l'op{\´e}rateur de Dirac},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-5644},
  year      = {2003},
  abstract  = {Nous {\´e}tablissons une nouvelle majoration optimale pour les plus petites valeurs propres de l'op{\´e}rateur de Dirac sur une hypersurface compacte de l'espace hyperbolique.},
  language  = {fr}
}
@misc{DevchandNuytsWeingart2009,
  author    = {Devchand, Chandrashekar and Nuyts, Jean and Weingart, Gregor},
  title     = {Matryoshka of special democratic forms},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {841},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-42900},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-429002},
  pages     = {545 -- 562},
  year      = {2009},
  abstract  = {Special p-forms are forms which have components fµ1…µp equal to +1, -1 or 0 in some orthonormal basis. A p-form ϕ ∈ � pRd is called democratic if the set of nonzero components {ϕμ1...μp} is symmetric under the transitive action of a subgroup of O(d,Z) on the indices {1, . . . , d}. Knowledge of these symmetry groups allows us to define mappings of special democratic p-forms in d dimensions to special democratic P-forms in D dimensions for successively higher P = p and D = d. In particular, we display a remarkable nested structure of special forms including a U(3)-invariant 2-form in six dimensions, a G2-invariant 3-form in seven dimensions, a Spin(7)-invariant 4-form in eight dimensions and a special democratic 6-form O in ten dimensions. The latter has the remarkable property that its contraction with one of five distinct bivectors, yields, in the orthogonal eight dimensions, the Spin(7)-invariant 4-form. We discuss various properties of this ten dimensional form.},
  language  = {en}
}
@misc{DaiPraLouisMinelli2006,
  author    = {Dai Pra, Paolo and Louis, Pierre-Yves and Minelli, Ida},
  title     = {Monotonicity and complete monotonicity for continuous-time Markov chains},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-7665},
  year      = {2006},
  abstract  = {We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in continuous time but not in discrete-time.},
  subject      = {Stochastik},
  language  = {en}
}
@misc{ChechkinZaidLomholtetal.2013,
  author    = {Chechkin, Aleksei V. and Zaid, Irwin M. and Lomholt, Michael A. and Sokolov, Igor M. and Metzler, Ralf},
  title     = {Bulk-mediated surface diffusion on a cylinder in the fast exchange limit},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {593},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-41548},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-415480},
  pages     = {114 -- 126},
  year      = {2013},
  abstract  = {In various biological systems and small scale technological applications particles transiently bind to a cylindrical surface. Upon unbinding the particles diffuse in the vicinal bulk before rebinding to the surface. Such bulk-mediated excursions give rise to an effective surface translation, for which we here derive and discuss the dynamic equations, including additional surface diffusion. We discuss the time evolution of the number of surface-bound particles, the effective surface mean squared displacement, and the surface propagator. In particular, we observe sub- and superdiffusive regimes. A plateau of the surface mean-squared displacement reflects a stalling of the surface diffusion at longer times. Finally, the corresponding first passage problem for the cylindrical geometry is analysed.},
  language  = {en}
}
@misc{ChampagnatRoelly2008,
  author    = {Champagnat, Nicolas and Roelly, Sylvie},
  title     = {Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-18610},
  year      = {2008},
  abstract  = {A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every finite time interval, its distribution is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. Several results on the long time behavior of the conditioned mass process - the conditioned multitype Feller branching diffusion - are then proved. The general case is first considered, where the mutation matrix which models the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are analyzed too .},
  language  = {en}
}