September 2007 - February 2008
Organizers: Sergio Albeverio, Jennifer Chayes, Gerard Ben Arous, Michel Ledoux, Karl Theodor Sturm
Description: Applied stochastic models are frequently very complex, high or infinite dimensional, with a mixture of discrete and continuous elements, singularities and nonlinearities. Their mathematical description and analysis often requires a combination of methods from discrete probability and combinatorics, stochastic analysis, partial differential equations, and geometric analysis. For example, discretization of the continuous components of a stochastic model is fundamental for numerical simulations. Conversely, continuum limits can be helpful to gain a better understanding of discrete models, e.g. in statistical mechanics. Powerful techniques, e.g. logarithmic Sobolev inequalities and concentration of measure estimates have originally been developed in a continuous setup, partially motivated by geometric considerations. Nowadays they are of rapidly increasing importance also in discrete setups, in the analysis of asymptotic and non-asymptotic issues of stochastic processes like the rate of convergence to equilibrium, and for various algorithmic applications. The extension of concepts from geometric stochastic analysis to singular spaces, graphs and random structures is a major challenge. A better understanding of the fascinating connections between random matrices and number theory requires a combination of probability, geometric analysis and algebra.
Hence there are clear needs to increase significantly the interaction between stochastic analysis and non-linear partial differential equations on the one side, and discrete probability and theoretical computer science on the other side. The aim of this program was to bring together scientists from these different communities, and thus to boost new developments. A particular emphasis was given to training of postdocs and PhD students in this important field. This is reflected in a high number of introductory courses by leading top-level scientists. The program also addressed to young researchers from neighboring fields such as analysis and computer science.
Associated Events:
Workshop 1: Stochastic processes and algorithms
Workshop 2: Stochastic calculus on manifolds, graphs, and random structures
Workshop 3: Particle systems, nonlinear diffusions, and equilibration
Workshop 4a: Random matrices and number theory
Workshop 4b: Random matrices - probabilistic aspects and applications
Workshop 5: Finance, Stochastics, Insurance
| No. | Author(s) | Title | Preprint | Publication |
| 2007c01 | Barlow, M. T.; Grigor'yan, A.; Kumagai, T. | Heat kernel upper bounds for jump processes and the first exit time | J. Reine Angew. Math. 626 (2009), 135–157. https://doi.org/10.1515/CRELLE.2009.005 |
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| 2007c02 | Goldberg, L. A.; Jerrum, M.; Karpinski, M. | The mixing time of Glauber dynamics for coloring regular trees | 0806.0921 | Random Structures Algorithms. 36(4) (2010), 464–476. https://doi.org/10.1002/rsa.20303 |
| 2007c03 | Grigor'yan, A.; Kumagai, T. | On the dichotomy in the heat kernel two sided estimates | Analysis on graphs and its applications, 199–210. https://doi.org/10.1090/pspum/077/2459870 |
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| 2007c04 | Eberle, A.; Marinelli, C. | Quantitative approximations of evolving probability measures and sequential Markov chain Monte Carlo methods | 1010.1696 | Probab. Theory Related Fields. 155(3-4) (2013), 665–701. https://doi.org/10.1007/s00440-012-0410-y |
| 2007c05 | Hambly, B. M.; Kumagai, T. | Diffusion on the scaling limit of the critical percolation cluster in the diamond hierarchical lattice | Comm. Math. Phys. 295(1) (2010), 29–69. https://doi.org/10.1007/s00220-009-0981-3 |
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| 2007c06 | Ivanyos, G.; Karpinski, M.; Saxena, N. | Schemes for deterministic polynomial factoring | 0804.1974 | ISSAC 2009. 191–198. https://doi.org/10.1145/1576702.1576730 |
| 2007c07 | Ivanyos, G.; Karpinski, M.; Rónyai, L.; Saxena, N. | Trading GRH for algebra: algorithms for factoring polynomials and related structures | 0811.3165 | Math. Comp. 81(277) (2012), 493–531. https://doi.org/10.1090/S0025-5718-2011-02505-6 |
| 2007c08 | Ivanyos, G.; Karpinski, M.; Saxena, N. | Deterministic polynomial time algorithms for matrix completion problems | 0907.0774 | SIAM J. Comput. 39(8) (2010), 3736–3751. https://doi.org/10.1137/090781231 |
| 2007c09 | Karpinski, M.; Schudy, W. | Approximation schemes for the betweenness problem in tournaments and related ranking problems | 0911.2214 | Approximation, randomization, and combinatorial optimization, 277–288. https://doi.org/10.1007/978-3-642-22935-0_24 |
| 2007c10 | Karpinski, M.; Schudy, W. | Linear time approximation schemes for the Gale-Berlekamp game and related minimization problems | 0811.3244 | STOC'09, 313–322. https://doi.org/10.1145/1536414.1536458 |
| 2007c11 | Shigekawa, I. | Dual ultracontractivity and its applications | Front. Math. China. 9(4) (2014), 899–928. https://doi.org/10.1007/s11464-014-0398-y |
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| 2007c12 | Baudoin, F.; Hairer, M.; Teichmann, J. | Ornstein-Uhlenbeck processes on Lie groups | 0711.2419 | J. Funct. Anal. 255(4) (2008), 877–890. https://doi.org/10.1016/j.jfa.2008.05.004 |
Name |
Affiliation |
| Louis-Pierre Arguin | New York University |
| Martin Barlow | University of British Columbia |
| Tomas Björk | Stockholm School of Economics |
| Christian Borgs | Microsoft Research |
| Anton Bovier | Universität Bonn |
| Eric A. Carlen | School of Mathematics Georgia |
| Abdoulaye Coulibaly | Université de Poitiers |
| Abdoulaye Coulibaly | Université de Poitiers |
| Lukasz Derdziuk | Universität Bielefeld |
| David Elworthy | University of Warwick |
| Dmitri Finkelshtein | Institute of Mathematics, Kyiv |
| Delphine Féral | Universitè Paul Sabatier |
| Stefan Wolfgang Grosskinsky | University of Warwick |
| Alice Guionnet | Ecole Normale Superieure de Lyon |
| Erwan Hillion | University of Bristol |
| James Inglis | Imperial College London |
| Mark Jerrum | Queen Mary University of London |
| Liza Jones | University of Bristol |
| Yuri Kondratiev | Universität Bielefeld |
| Maxim Kontsevich | Institut des Hautes Etudes Scientifiques |
| Oleksandr Kutovyi | Universität Bielefeld |
| Mikhail Langovoy | Universität Göttingen |
| Malwina Luczak | London School of Economics |
| Piotr Lugiewicz | University of Wroclaw |
| Daniel Rudolf | Friedrich-Schiller-Universität Jena |
| Barbara Rüdiger | Universität Koblenz |
| Christian Selinger | University of Luxembourg |
| Max Skipper | University of Oxford |
| Sven Struckmeier | Universität Bielefeld |
| Vladislav Vysotsky | St.Petersburg State University |
| Ying Wang | Max-Planck-Institut für Mathematik in den Naturwissenschaften |
| Lihu Xu | EURANDOM |
| Yuxin Yang | University of Warwick |
| Miaomiao Zhu | Max-Planck-Institut für Mathematik in den Naturwissenschaften |
This list does not include people who only participated in the workshops.
