Publications

1990

  1. Cox, J.T. and Greven, A.
    The Longterm Behaviour of Some Finite Particle Systems,
    Prob. Theory and Rel.Fields, 85, 195-237
  2. Greven, A.
    Symmetric Exclusion on Random Sets and a Related Problem for Random Walks in Random Environment.
    Prob. Theory and Rel. Fields, 85, 307-364

 


1991

  1. Greven, A.
    Phase Transition for the Coupled Branching Process. Part I: The ergodic theory in the range of finite second moments.
    Prob. Theory and Rel. Fields 87, 417-458
  2. Greven, A. and den Hollander, F.,
    Branching Random Walk in Random Environment. I. Phase diagram and variational problem,
    Journal of Statistical Physics, Vol. 65, Nos. 5/6, 1123-1146
  3. Greven, A. and den Hollander, F.,
    Branching Random Walk in Random Environment. II. Wavefront Propagation.
    Journal of Statistical Physics, Vol. 65, Nos. 5/6, 1147-1154
  4. Cox, J.T. and Greven, A.
    On the longterm behaviour of Finite Particle Systems: A Critical Dimension Example.
    Progress in Probability, Vol. 28. R. Durrett, H. Kesten, eds., 203-214

Arrow


1992

  1. Greven, A. and den Hollander, F.,
    Branching Random Walk in Random Environment: Phase Transition for Local and Global Growth rates.
    Prob. Theory and Related Fields, 91 (2); 195-250
  2. Fleischmann, K. and Greven, A.
    Localisation and Selection for a Mean Field Branching Random Walk in Random Environment.
    Ann. Prob., Vol. 20, no. 4, 2141-2163

Arrow


1993

  1. Baillon, B., Clement, Ph., den Hollander, F., and Greven, A.
    A Variational Formula for Branching Random Walk in Random Environment.
    Ann. Prob. Vol. 21, no. 1
  2. Dawson, D.A., and Greven, A.
    Multiple Time Scale Analysis of Hierarchically Interacting Systems.
    Stochastic Processes, A Festschrift in Honor of Gopinath Kallianpur. S. Cambanis, J.K. Gosh, R.L. Karandikar, P.K. Sen Eds., Springer, 51-59
  3. Dawson, D.A., and Greven, A.
    Multiple scale analysis of interacting diffusions.
    Prob. Theory Rel. Fields, 95, 467-508
  4. Dawson, D.A., and Greven, A.
    Hierarchical models of interacting diffusions: multiple time scales, phase transitions and clusterformation.
    Prob. Theory Rel. Fields, 96, 435-473
  5. Greven, A. and den Hollander, F.
    Variational characterisation of the speed of a one-dimensional self-repellent random walk.
    Ann. of Applied Prob., Vol. 3, No. 4, 1067-1099
  6. Cox, J.T. Bramson, M., and Greven, A.
    Ergodicity of critical spatial branching processes in low dimensions,
    Ann. Probab., 21, 1946-1957

Arrow


1994

  1. Cox, J.T. and Greven, A.
    Ergodic theorems for systems of locally interacting diffusions.
    Ann. of Prob. 22(2). 833-853
  2. Cox, J.T. and Greven, A.
    The finite systems scheme: An abstract theorem and a new example,
    Proceedings of CRM Conference on Measure valued processes, Stochastic partial differential equation and interacting Systems. CRM Proceedings and Lecture Notes of the American Mathematical Society. Vol. 5, 55-68, 1994.
  3. Greven, A.
    Coupling in the theory of interacting systems.
    Acta Applicandae Mathematicae, 34, 17-35
  4. Greven, A. and den Hollander, F.
    Large Deviations for a random walk in random environment.
    Ann. Prob. 22, No. 3, 1381-1428
  5. Baillon, B., Clement, Ph., den Hollander, F, and Greven, A.
    On a variational problem for an infinite particle system in a random medium. Part I: The global growth rate.
    Journal Reine und Angewandte Mathematik 454, 181-217
  6. Fleischmann, K. and Greven, A.
    Diffusive clustering in an infinite system of hierarchically interacting Fisher-Wright diffusions.
    Prob. Theory Rel. Fields. 98, 517-566
  7. Greven, A. and den Hollander, F.
    On a variational problem for an infinite particle system in random medium. Part II: The local growth rate.
    Prob. Theory Rel. Fields. 100, 301-328

Arrow


1995

  1. Baillon, B., Clément, Ph., den Hollander, F. and Greven, A.
    On the attracting orbit of a nonlinear transformation arising from renormalisation of hierarchically interacting diffusions. Part I: The compact case
    Can. J. of Math. Vol. 47, 3-27
  2. Cox, J.T., Greven, A. and Shiga, T.,
    Finite and infinite systems of interacting diffusions.
    Prob. Theory and Rel. Fields, 103, 165-197
  3. Dawson, D.A., Greven, A. and Vaillancourt, J.,
    Equilibria and quasi-equilibria for infinite systems of Fleming-Viot processes.
    Transactions of the American Math. Society, Vol. 347, Number 7, 2277-2361
  4. Cranston, M., and Greven, A.
    Coupling and harmonic functions for Markov processes in continuous time.
    Stochastic Processes and Their Applications, Vol. 60, Number 2, 261-286

Arrow


1996

  1. Fleischmann, K. and Greven, A.,
    Time-Space Analysis of the Cluster-Formation in Interacting Diffusions,
    EJP, Vol.1, Paper 6, 1-46 pages.
  2. Cox, T., Fleischmann, K., Greven, A.,
    Comparison of interacting diffusions and an application to their ergodic theory,
    Probability Theory Rel. Fields, 105, 513-528.
  3. Dawson, D.A. and Greven, A.,
    Multiple Space-Time Scale Analysis For Interacting Branching Models,
    EJP, Vol.1, Paper 14, 1-84 pages.

Arrow


1997

  1. Baillon, U.B., Clément, Ph., Greven, A., den Hollander, F.,
    On the attracting orbit of a nonlinear transformation arising from renormalisation of hierarchically interacting diffusion. Part II: The noncompact case,
    J. of Funct. Anal., vol. 146, (1), 236-298.
  2. Bramson, M., Cox, T., Greven, A.
    Invariant measures of critical spatial branching processes in high dimensions.
    Ann. Prob. Vol. 25, No. 1, 56-70.

Arrow


1998

  1. Cox, T., Greven, A. Shiga, T.,
    Finite and infinite systems of interacting diffusions. Part II.
    Math. Nachrichten 192, 105-124 (1998) (ps.file)

Arrow


1999

  1. Dawson, D. A., Greven, A.,
    Hierarchically interacting Fleming-Viot processes with selection and mutation: Multiple space time scale analysis and quasi-equilibria,
    EJP, Vol.4 , paper 4 , 1-81 pages (1999)
  2. Greven, A., Klenke, A., Wakolbinger, A.,
    The longtime behaviour of branching random walk in a catalytic medium
    EJP, Vol.4 , paper 12, 1-80 pages

Arrow


2000

  1. Greven, A., Hochberg, K.,
    New Behavioral Patterns for Two-Level Branching Systems,
    Stochastic models, Gorostizza, Ivanov, eds. CMS Conference Proceedings, Vol. 26, 205-215 (2000) (ps.file(proceedings))
  2. Greven, A.,
    On phase-transitions in spatial branching systems with interaction,
    Stochastic models, Gorostizza, Ivanov, eds. CMS Conference Proceedings, Vol. 26, 173-204 (2000) (ps.file)  
  3. Greven, A.
    Renormalization analysis of interacting spatial stochastic systems
    Proceedings of the Academy Colloquium "Infinite-dimensional stochastic analysis", 11-12 February, 1999, Amsterdam, Eds. Ph. Clement, F. den Hollander, J. van Neerven and B. de Pagter, (ps.file)
  4. Greven, A.
    Interacting stochastic systems: Longtime behavior and its renormalization analysis Jber. d. Dt. Math.-Verein. Vol. 102/4, 149-170.

Arrow


2001

  1. Greven A., Klenke A., Wakolbinger A.,
    Interacting Fisher-Wright diffusions in a catalytic medium
    Probab. Theory Relat. Fields 120, 1, 85-117. (dvi.file)

Arrow


2002

  1. Greven A., Klenke A., Wakolbinger A.,
    Interacting diffusions in a random medium: Comparison and longtime behavior
    Stochastic Process Appl. Vol. 98, 23-41.

Arrow


2003

  1. Dawson, D.A., Greven, A.
    State dependent multi-type spatial branching processes and their longtime behavior,
    EJP Vol. 8 (4), 1-93.

Arrow


2004

  1. Cox, J. T., Dawson, D. A., Greven, A.,
    Mutually catalytic super branching random walks: Large finite systems and renormalization analysis, 97 pages
    Memoirs of the AMS, Vol. 171, No. 809

Arrow


2005

  1. Greven A., Limic, V., Winter A.,
    Representation theorems for Interacting Fisher-Wright Diffusions and Applications,
    Electronic J. of Probab., Vol. 10, No. 39

Arrow


2006

Arrow


2007

  1. Greven A., den Hollander F.,
    Phase transitions for the long-time behavior of interacting diffusions,
    Annals of Probability, Vol. 35, No. 4 (1250-13-6)

Arrow


2008

  1. Dawson, D. A., Greven, A., den Hollander F., Sun R., Swart S.,
    The renormalization transformation for two-type branching models,
    to appear in the Annales de l'Institute Henri Poincare 2008 Probabilités et Statistiques 44, 1038--1077, 2008


Arrow


2009

  1. Greven A., Popovic L., Winter A.,
    Genealogy of catalytic branching models,
    Annals of Applied Probability, Vol. 19, No. 3, 1232--1272, 2009
  2. Greven A., Pfaffelhuber P., Winter A.,
    Convergence in distribution of random metric measure spaces (The $\Lambda$-coalescent measure tree)
    Prob. Theo. Rel. Fields, Vol. 145, issue 1, P. 285--322, 2009
  3. Greven, A., Hochberg K.,
    On the use of the Laplace Functinal for Two-Level Branching Systems,
    International Journal of Pure and Applied Mathematics, Vol. 55, No. 2, 2009

Arrow


2010

  1. Birkner M., Greven A., den Hollander F.,
    Quenched LDP for words in a letter sequence,
    Prob. Theo. Rel. Fields, Vol. 148, no. 3/4, P. 403-456 (2010)
  2. Greven A., Pfaffelhuber P., Winter A.,
    Tree-valued resampling dynamics: Martingale problems and appications
    (submitted to PTRF 2010)


Arrow


2011

  1. Birkner M., Greven A., den Hollander F.,
    Collision local time of transient random walks and intermediate phases in interacting stochastic systems, EJP, Vol. 16, 552--586, 2011.

  2. Depperschmidt A., Greven A., Pfaffelhuber P.
    Marked metric measure spaces, Elect. Comm. in Probab., Vol. 16, 174--188, 2011

  3. D. A. Dawson, A. Greven,
    Multiscale analysis: Fisher-Wright diffusions with kare mutations and selection, logistic branching system, (accepted for Festschrift for Juergen Gaertner and Erwin Bolthausen, el. version on Arxiv.org, Springer Verlag 2011)

  4. Depperschmidt A., Greven A., Pfaffelhuber P.
    Tree-valued Fleming-Viot dynamics with mutation and selection, Submitted to Annals of Probability 2011.

  5. Greven A., Limic, V., Winter A.,
    Coalescent processes arising in a study of diffusive clustering, (submitted to EJP in 2011)

  6. D. A. Dawson and A. Greven,
    Invasion by rare mutants in a spatial two-type Fisher-Wright system with selection, arXiv 1104.0253 (2011)

  7. D. A. Dawson and A. Greven,
    Duality for spatially interacting Fleming-Viot processes with mutation and selection, arXiv:1104.1099 (2011)

    In preparation 2011

  8. Greven A., den Hollander F., Kliem S., Klymovskiy A.,
    Renormalisation of hierarchically interacting $\Lambda$-Cannings processes
    (In preparation 2011)

  9. Cox T., Greven A.,
    The typical tree in a contact process,
    (In preparation 2011)
  10. Dawson D. A., Greven A.,
    Renormalization analysis of multitype state depending branching diffusions,
    (In preparation 2011)
  11. Dawson, D. A., Greven, A.
    On the effects of migration in spatial Fleming-Viot models with selection and mutation
    (In preparation 2011)

    Work in progress

  12. Dawson D. A., Greven A., Zähle I.,
    Continuum limits of multitype population models and renormalization,
    (In preparation 2011)
  13. del Moral P., Greven A.,
    Moran population models and genetic algorithm chains,
    (In preparation 2011)
  14. Depperschmidt, A., Greven A.,Pfaffelhuber P.,
    Tree-valued Fleming-Viot dynamics with selection,
    (submitted to Annals of Probability 2011)
  15. Eckhoff, M., Greven A.,
    Comparison techniques for multi-dimensional interacting diffusions,
    (In preparation 2011)
  16. Geiger, J., Greven, A.,
    The spatial structure of the historical process of Branching Random Walk
    (In preparation 2011)
  17. Greven, A., Hochberg, K.,
    The longtime behavior of Multilevel Branching Systems,
    (In preparation 2011)
  18. Greven A., Klimovsky A.,
    Renormalization of interacting diffusions on $\Z^2$,
    (In preparation 2011)
  19. Greven A., Klimovsky A., Winter A.,
    Tree-valued Cannings dynamics
    (In preparation 2011)
  20. Greven A., Limic, V., Winter A.,
    Cluster formation in spatial Moran models in critical dimension via particle representation,
    (submitted to EJP, in revision 2010)
  21. Greven A., Limic, V., Winter A.,
    Cluster formation in Moran models on two-dimensional tori
    (In preparation 2011)
  22. Greven A., Pfaffelhuber P., Wakolbinger A.,
    Genetic hitchhiking in substructured populations,
    (In preparation 2011)
  23. Greven A., Pfaffelhuber P., Winter A.,
    Time-space structure of genealogies of spatial Moran models and applications to interacting Fisher-Wright diffusions,
    (In preparation 2011)
  24. Greven A., Pfaffelhuber P., Sturm A., Winter A., Zähle I.,
    A multitype spatial branching model for local self-regulation,
    (In preparation 2011)
  25. Greven A., Popovic L., Winter A.,
    Genealogical forests of catalytic branching random walks in the diffusion limit,
    (In preparation 2011)
  26. Greven A., Sun R., Winter A.,
    Limit genealogies of interacting Fleming-Viot processes on $\Z^1$,
    (In preparation 2011)