Prof. Dr. Wolfgang König

Berlin-Leipzig Seminar on Analysis and Probability Theory

Regular seminar of the DFG Research group Analysis and Stochastics in Complex Physical Systems, Berlin and Leipzig

Past meeting: Friday, 4 November, 2011

Seminarraum A

9:00 - 10:50: Miguel Ballesteros (TU Braunschweig) Existence and construction of resonances for atoms coupled to the quantized radiation field The theory of quantum mechanics asserts that the energy of an atom can be quantized. The possible energies are the eigenvalues of the Schr\"odinger equation. The lowest eigenvalue is called the ground state energy and the other eigenvalues are the excited energies. The Schr\"odinger equation predicts that if an atom is in an excited state at some time then it remains in that state forever. Experiments show, however, that the atom does not remain in an excited state forever, but decays to a lower energy state. During this decay, the atom emits photons whose energy is given by the difference between the initial and the final energy, in accordance with the Bohr's frequency condition. The process described above can be expressed on a technical level as follows: the atom remains in a certain state for a short period and then decays to a lower energy state. Thus the excited states are not eigenvalues of a certain Hamiltonian but turn into \emph{resonances}. These resonances appear when the photon field is introduced into the picture. We analyze the Pauli-Fierz model, which represents a non-relativistic atom coupled to a (quantized) photon field. We prove that the excited eigenvalues of the atom give rise to resonances, once the photon field is introduced, and that the energies of the resonance-producing photons are given by Bohr's frequency condition, up to second order in the coupling constant. We do not assume that there is an infrared regularization but we require an ultraviolet cutoff. We review Sigal's recent construction of resonances based on renormalization group analysis and present a novel alternative construction based on ``Pizzo's Method''. This is a joint work with Volker Bach, Alessandro Pizzo and Marwan Shoufan. 11:00 - 11:50: Jonas Tölle (TU Berlin) Singular stochastic evolution inclusions and ergodicity We provide an abstract variational existence and uniqueness result for multi-valued monotone non-coercive stochastic evolution inclusions in Hilbert spaces with general additive noise and Gaussian multiplicative noise. In particular, we consider stochastic diffusion inclusions of the type \[\tag{1}\left\{\begin{aligned}dX_t\in\left\{\begin{aligned}&\operatorname{div}[\phi(\nabla X_t)]\\ &L[\psi(X_t)]\end{aligned}\right\}\,dt&+\left\{\begin{aligned}&dN_t\\ &B_t(X_t)\,dW_t\end{aligned}\right.\\ X_0&=x, \end{aligned}\right.\] where $\phi\subset\mathbb{R}^d\times\mathbb{R}^d$, $\psi\subset\mathbb{R}\times\mathbb{R}$ are cyclically monotone graphs with sublinear growth (possibly the Heaviside function), $L$ is a dissipative Markov operator, $\{N_t\}$ is a general space-regular c\`adl\`ag process, $\{B_t(\cdot)\}$ is a family of Hilbert-Schmidt operators, $\{W_t\}$ is a cylindrical Wiener process. The initial condition $x$ is chosen either in $L^2$ or some negative order Sobolev space associated to $L$. The solutions to (1) depend continuously on $\phi$ and $\psi$ with respect to convergence of graphs (that is, pointwise convergence of their primitives). For equations (1), in the case of additive Wiener noise, we prove the existence of a unique invariant measure (for all space dimensions) which is weak$^\ast$ mean ergodic if we assume suitable Sobolev embeddings. Applications to random dynamical systems for noise with stationary increments are also discussed. (Joint work with Benjamin Gess, Bielefeld) 12:00 - 12:50: Georg Weiss (Universität Düsseldorf) Pulsating waves in self-propagating high temperature synthesis We derive the precise limit of SHS in the high activation energy scaling suggested by B.J. Matkowksy-G.I. Sivashinsky in 1978 and by A. Bayliss -- B.J. Matkowksy -- A.P. Aldushin in 2002. In the time-increasing case the limit coincides with the Stefan problem for supercooled water with spatially inhomogeneous coefficients. In general it is a nonlinear forward-backward parabolic equation with discontinuous hysteresis term. In the first part of the talk we give a complete characterization of the limit problem in the case of one space dimension. In the second part we construct in any finite dimension a rather large family of pulsating waves for the limit problem. In the third part, we prove that for constant coefficients the limit problem in any finite dimension does not admit non-trivial pulsating waves. The combination of all three parts strongly suggests a relation between the pulsating waves constructed and the numerically observed pulsating waves for finite activation energy in dimension $n\ge 1$ and therefore provides a possible and surprising explanation for the phenomena observed. (joint work with Regis Monneau, CERMICS) Printable announcements: 4 November, 2011 (ps), 4 Novembe, 2011 (pdf)

Past meeting: Friday, 8 July, 2011

Seminarraum A

9:30 - 10:20: Margit Rösler (TU Clausthal) Multivariable special functions and symmetries 10:30 - 11:20: Wolfgang König (Weierstrass Institute Berlin and TU Berlin) Eigenvalue order statistics and mass concentration in the parabolic Anderson model 11:30 - 12:20: Paul Jung (Sogang University, Seoul) Random-time transformations and fractional stable motions Printable announcements: 8 July, 2011 (ps), 8 July, 2011 (pdf)

Last meeting: Friday, 14 January, 2011

Room 611

10:15 - 11:05: Ben Schweizer (Technical University Dortmund) On the homogenization of Prandtl-Reuss plasticity equations 11:15 - 12:05: Friedrich Götze (University Bielefeld) Approximations in free and classical central limit theorems Printable announcements: 14 Jan, 2011 (ps), 14 Jan, 2011 (pdf)

Past meeting: Friday, 26 November, 2010

Room A01

10:00 - 10:50: Benjamin Schlein (University of Bonn) Effective evolution equations from many body quantum dynamics 11:00 - 11:50: Noam Berger (Hebrew University of Jerusalem) Spin-glasses on $\Z^2$ - Many questions, very few answers 12:00--12:50: Sergio Conti (University of Bonn) On geometrically nonlinear plasticity models in the limit of rigid elasticity Printable announcements: 26 Nov, 2010 (ps), 26 Nov, 2010 (pdf)

Past meeting: Friday, 9 July, 2010

Room MA 313

Seminar room

9:40 - 10:30: Michel Ledoux (University of Toulouse) The geometry of convolution inequalities 10:40 - 11:30: Dorothee Knees (Weierstrass Institute Berlin) On the vanishing viscosity method in fracture mechanics 11:40--12:30: Erwin Bolthausen (TU Berlin, on leave from University of Zurich) On the ultrametricity problem in spin glass theory Printable announcements: 9 July, 2010 (ps), 9 July, 2010 (pdf)

Last meeting: Friday, 18 June, 2010

University of Heidelberg, Institute for Theoretical Physics, Philosophenweg 19, 69120 Heidelberg.

Seminar room

10:15 - 11:15: Wojciech de Roeck (University of Heidelberg) Diffusion in Hamiltonian systems 11:30--12:30: Christof Külske(University of Bochum) Spin dynamics, generalized Gibbs measures and multiple histories Printable announcements: 18 June, 2010 (ps), 15 June, 2010 (pdf)

Last meeting: Friday, 15 January, 2010

University of Bonn, Institute for Applied Mathematics, Endenicher Str. 60, 53115 Bonn

Lipschitz Lecture Hall

9:40 - 10:30: Jason Miller (Stanford University) Fluctuations for the Ginzburg-Landau grad-phi interface model on bounded fomains 10:40--11:30: Felix Otto (University of Bonn) Optimal error estimates in stochastic homogenization 11:40-12:30: Annibale Magni (University of Dortmund) Perelman's Dilaton Printable announcements: 15 January, 2010 (ps), 15 January, 2010 (pdf)

Past meeting: Friday, 27 November, 2009

Technical University Berlin, Institute for Mathematics, Str. des 17. Juni 136, 10623 Berlin

Room 315 (Matheon-Lounge)

9:40 - 10:30: Bernd Metzger (Weierstraß Institute Berlin) The Gross-Pitaevskii functional with a random background potential and condensation in the single particle ground state 10:40--11:30: Errico Presutti (University of Rome II Tor Vergata) Phase transitions in continuum 11:40-12:30: Jean-Dominique Deuschel (Technical University Berlin) Hydrodynamic limit for interface model with non-convex interaction Printable announcements: 27 November, 2009 (ps), 27 November, 2009 (pdf)

Past meeting: Friday, 26 June, 2009

Technical University Berlin, Institute for Mathematics, Str. des 17. Juni 136, 10623 Berlin

Room 313/314

9:40 - 10:30: Hans-Otto Georgii (Ludwig-Maximilians-Universität München) Variational characterisation of Gibbs measures with Delaunay triangle interaction 10:40--11:30: Bernd Schmidt (Technische Universität München) On a semilinear variational problem 11:40-12:30: Laszlo Erdös (Ludwig-Maximilians-Universität München) Bulk universality for Wigner matrices Printable announcements: 26 June, 2009 (ps), 26 June, 2009 (pdf)

Past meeting: Friday, 17 April, 2009

Max Planck Institute, Inselstr. 22, 04103 Leipzig

Room A01

9:40 - 10:30: Abdelhadi Es-Sarhir (Technical University Berlin) A priori estimates of invariant measures for semilinear SPDE's and applications 10:40--11:30: Marek Biskup (University of South Bohemia Ceske Budejovice) Gradient models with non-convex interactions 11:40-12:30: Stefan Adams (Warwick University, MPI Leipzig and LMU Munich) Strict convexity of the surface tension of Gradient models with non-convex interactions Printable announcements: 17 April, 2009 (ps), 17 April, 2009 (pdf)

Past meeting: Friday, 12 December, 2008

Technical University Berlin, Institute for Mathematics, Str. des 17. Juni 136, 10623 Berlin

Room 313/314

9:40 - 10:30: Mark Peletier (University of Technology Eindhoven) Unification of diffusion and reaction: derivation of the law of mass action 10:40--11:30: Utpal Manna (MPI Leipzig) An Application of Stochastic Stackelberg Differential Games in Conflict Management 11:40-12:30: Reinhold Schneider (TU Berlin) Analysis of the projected Coupled Cluster Method in Electronic Structure Calculation Printable announcements: 12 December, 2008 (ps), 12 December, 2008 (pdf)

Last meeting: Friday, 24 October, 2008

Room A01

9:30 - 10:20: Patrick Dondl (MPI Leipzig) Pinning and depinning behavior of martensitic phase boundaries in a heterogeneous environment 10:30--11:20: Nicolas Petrelis (TU Berlin) Copolymer in an emulsion: supercritical and subcritical regime. 11:30-12:20: Rene Schilling (TU Dresden) Approximating Feller processes Printable announcements: 24 October, 2008 (ps), 24 October, 2008 (pdf)

Past meeting: Friday, 20 June, 2008

Room MA313/314

9:40 - 10:30: Enzo Olivieri (Universita Roma Due Tor Vergata) Escape from metastability for conservative dynamics at low temperature 10:40--11:30: Valentin A. Zagrebnov (Universite de la Mediterrane and Centre de Physique Theorique Marseille) Bose-Einstein condensation in external potentials 11:40-12:30: Joe Pule (University College Dublin) Long cycles and Bose-Einstein condensation in the infinite-range-hopping Bose-Hubbard model Printable announcements: 20 June, 2008 (ps), 20 June, 2008 (pdf)

Past meeting: Friday, 18 April, 2008

Room A01

9:30 - 10:20: Martin Hairer (Warwick University) Slow energy dissipation in anharmonic chains 10:30--11:20: Sabine Jansen (University of Leipzig) Thermodynamic limit for jellium on a cylinder 11:30-12:20: Stefan Großkinsky (Warwick University) Equivalence of ensembles and condensation in zero-range processes Printable announcements: 18 Apr, 2008 (ps), 18 Apr, 2008 (pdf)

Past meeting: Friday, 8 February, 2008

Room 313/314

9:40 - 10:30: Michael Röckner (University of Bielefeld and Purdue University) Self-organized criticality via SPDE 10:40--11:30: Michael Scheutzow (Technical University Berlin) Global properties of stochastic flows on Euclidean spaces 11:40-12:30: Elisabetta Scoppola (University of Rome Tre) Some spin glass ideas applied to the clique problem Printable announcements: 8 Feb, 2008 (ps), 8 Feb, 2008 (pdf)

Past meeting: Friday, 11 January, 2008

Room A01

9:30 - 10:20: Franz Merkl (University of Munich) Linearly edge-reinforced random walks 10:30--11:20: Karl-Theodor Sturm (University of Bonn) Entropic measure and Wasserstein diffusion 11:30-12:20: Georg Dolzmann (University of Regensburg) Material systems with orientational degrees of freedom Printable announcements: 11 Jan, 2008 (ps), 11 Jan, 2008 (pdf)

Past meeting: Friday, 30 November, 2007

Room MA 313/314

9:50 - 10:40: Noemi Kurt (University of Zurich) A Gaussian interface model with Laplacian interactions in the critical dimension 10:50--11:40: Fabio Toninelli (University of Lyon) Disordered pinning models: beyond annealed bounds 11:50-12:40: Milos Zahradnik (Charles University of Prague) A purely combinatorial approach to cluster expansions Printable announcements: 30 Nov, 2007 (ps), 30 Nov, 2007 (pdf)

Past meeting: Friday, 13 July, 2007

Room G10

9:30 - 10:20: Anna de Masi (Aquila) Ergodic properties of Gibbs measures with constraints 10:30--11:20: Günther Grün (Erlangen) Thin-film flow influenced by thermal fluctuations 11:30-12:20: Matthias Löwe (Münster) Critical fluctuations in the Hopfield model Printable announcements: 13 July, 2007 (ps), 13 July, 2007 (pdf)

Past meeting: Friday, 15 June, 2007

Room MA313/314

9:40 - 10:30: Manfred Salmhofer (Leipzig) Determinant bounds and the Matsubara UV problem of many-fermion systems 10:40--11:30: Frank Redig (Leiden) 11:40-12:30: Florian Theil (Warwick) To be announced Printable announcements: 15 June, 2007 (ps), 15 June, 2007 (pdf)

Past meeting: Friday, 9 February, 2007

Room A01

10:30 - 11:30: Karel Netocny (Prague) Towards quantum large deviation theory 11:40--12:40: Jan Swart (Prague) The rebellious voter model 14:00-15:00: Felix Otto (Bonn) A new criterion for the logarithmic Sobolev inequality Printable announcements: 9 Feb, 2007 (ps), 9 Feb, 2007 (pdf)

Past meeting: Friday, 19 January, 2007

Room MA313/314

9:45 - 10:45: Thierry Bodineau (Paris) Current large deviations in stochastic systems 10:55--11:55: Nicolas Dirr (MPI MIS Leipzig) Sharp-interface limit of a mesoscopic energy with a random external field. 13:00-14:00 Senya Shlosman (Marseille) Condensation phenomenon in the equilibrium statistical mechanics Printable announcements: 19 Jan, 2007 (ps), 19 Jan, 2007 (pdf)

Past meeting: Friday, 1 December, 2006

Room A01

10:30 - 11:30: Lorenzo Zambotti (Paris) Stochastic models for the evolution of a small droplet on a wall 11:40--12:40: Andrea Braides (Rome) Variational problems with percolation 14:00-15:00: Volker Bach (Mainz) The renormalized electron mass and other topics in nonrelativistic quantum electrodynamics Printable announcements: 1 Dec, 2006 (ps), 1 Dec, 2006 (pdf)

Past meeting: Friday, 3 November, 2006

Room MA313/314

9:45 - 10:45: Rongfeng Sun (TU Berlin) The Brownian net 10:55--11:55: Codina Cotar (TU Berlin) Construction of a percolating hard sphere model 13:00-14:00 Richard James (University of Minnesota and MPI MIS Leipzig) New observations on the origins of hysteresis in phase transformations and metastability in the calculus of variations Printable announcements: 3 Nov, 2006 (ps), 3 Nov, 2006 (pdf)

Past meeting: Friday, 6 July, 2006

Felix Klein Lecture Hall (room 4-24),

10:30 - 11:30: Alexander Mielke (WIAS Berlin and HU Berlin) Multiple scales and Gamma limits in rate-independent material models 11:40 - 12:40: Stefan Adams (MPI Leipzig) Large deviations for long cycles and probabilistic approaches to Bose-Einstein condensation 14:00-15:00 Amir Dembo (Stanford University) Sequence and structure matching: applications of probability theory Printable announcements: 7 July, 2006 (ps), 7 July, 2006 (pdf)

Past meeting: Friday, 21 April 2006

Room MA415

10:15 - 11:15: Max von Renesse (TU Berlin) Stochastic heat equation in Wasserstein space as generalized Fleming-Viot process 11:25 - 12:25: Michiel van den Berg (Bristol University) Heat flow, Brownian motion and Hardy inequality for complete Riemannian manifolds 13:30-14:30 Anton Bovier (TU Berlin and Weierstrass Institute Berlin) Spectral approaches to ageing Printable announcements: 21 April, 2006 (ps), 21 April, 2006 (pdf)