Publications
1990
- Cox, J.T. and Greven, A.
The Longterm Behaviour of Some Finite Particle Systems,
Prob. Theory and Rel.Fields, 85, 195-237 - 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
- 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 - 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 - 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 - 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
1992
- 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 - 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
1993
- 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 - 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 - Dawson, D.A., and Greven, A.
Multiple scale analysis of interacting diffusions.
Prob. Theory Rel. Fields, 95, 467-508 - 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 - 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 - Cox, J.T. Bramson, M., and Greven, A.
Ergodicity of critical spatial branching processes in low dimensions,
Ann. Probab., 21, 1946-1957
1994
- Cox, J.T. and Greven, A.
Ergodic theorems for systems of locally interacting diffusions.
Ann. of Prob. 22(2). 833-853 - 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. - Greven, A.
Coupling in the theory of interacting systems.
Acta Applicandae Mathematicae, 34, 17-35 - Greven, A. and den Hollander, F.
Large Deviations for a random walk in random environment.
Ann. Prob. 22, No. 3, 1381-1428 - 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 - Fleischmann, K. and Greven, A.
Diffusive clustering in an infinite system of hierarchically interacting Fisher-Wright diffusions.
Prob. Theory Rel. Fields. 98, 517-566 - 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
1995
- 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 - Cox, J.T., Greven, A. and Shiga, T.,
Finite and infinite systems of interacting diffusions.
Prob. Theory and Rel. Fields, 103, 165-197
- 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 - 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
1996
- Fleischmann, K. and Greven, A.,
Time-Space Analysis of the Cluster-Formation in Interacting Diffusions,
EJP, Vol.1, Paper 6, 1-46 pages. - Cox, T., Fleischmann, K., Greven, A.,
Comparison of interacting diffusions and an application to their ergodic theory,
Probability Theory Rel. Fields, 105, 513-528. - Dawson, D.A. and Greven, A.,
Multiple Space-Time Scale Analysis For Interacting Branching Models,
EJP, Vol.1, Paper 14, 1-84 pages.
1997
- 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. - Bramson, M., Cox, T., Greven, A.
Invariant measures of critical spatial branching processes in high dimensions.
Ann. Prob. Vol. 25, No. 1, 56-70.
1998
- Cox, T., Greven, A. Shiga, T.,
Finite and infinite systems of interacting diffusions. Part II.
Math. Nachrichten 192, 105-124 (1998) (ps.file)
1999
- 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) - 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
2000
- 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)) - 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) - 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)
- Greven, A.
Interacting stochastic systems: Longtime behavior and its renormalization analysis Jber. d. Dt. Math.-Verein. Vol. 102/4, 149-170.
2001
- Greven A., Klenke A., Wakolbinger A.,
Interacting Fisher-Wright diffusions in a catalytic medium
Probab. Theory Relat. Fields 120, 1, 85-117. (dvi.file)
2002
- Greven A., Klenke A., Wakolbinger A.,
Interacting diffusions in a random medium: Comparison and longtime behavior
Stochastic Process Appl. Vol. 98, 23-41.
2003
- Dawson, D.A., Greven, A.
State dependent multi-type spatial branching processes and their longtime behavior,
EJP Vol. 8 (4), 1-93.
2004
- 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
2005
- Greven A., Limic, V., Winter A.,
Representation theorems for Interacting Fisher-Wright Diffusions and Applications,
Electronic J. of Probab., Vol. 10, No. 39
2006
2007
- 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)
2008
- 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
2009
- Greven A., Popovic L., Winter A.,
Genealogy of catalytic branching models,
Annals of Applied Probability, Vol. 19, No. 3, 1232--1272, 2009
- 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
- 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
2010
- 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)
- Greven A., Pfaffelhuber P., Winter A.,
Tree-valued resampling dynamics: Martingale problems and appications
(submitted to PTRF 2010)
2011
- 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.
- Depperschmidt A., Greven A., Pfaffelhuber P.
Marked metric measure spaces, Elect. Comm. in Probab., Vol. 16, 174--188, 2011
- 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)
- Depperschmidt A., Greven A., Pfaffelhuber P.
Tree-valued Fleming-Viot dynamics with mutation and selection, Submitted to Annals of Probability 2011.
- Greven A., Limic, V., Winter A.,
Coalescent processes arising in a study of diffusive clustering, (submitted to EJP in 2011)
- D. A. Dawson and A. Greven,
Invasion by rare mutants in a spatial two-type Fisher-Wright system with selection, arXiv 1104.0253 (2011)
- D. A. Dawson and A. Greven,
Duality for spatially interacting Fleming-Viot processes with mutation and selection, arXiv:1104.1099 (2011)
In preparation 2011
- Greven A., den Hollander F., Kliem S., Klymovskiy A.,
Renormalisation of hierarchically interacting $\Lambda$-Cannings processes
(In preparation 2011)
- Cox T., Greven A.,
The typical tree in a contact process,
(In preparation 2011)
- Dawson D. A., Greven A.,
Renormalization analysis of multitype state depending branching diffusions,
(In preparation 2011)
- 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
- Dawson D. A., Greven A., Zähle I.,
Continuum limits of multitype population models and renormalization,
(In preparation 2011)
- del Moral P., Greven A.,
Moran population models and genetic algorithm chains,
(In preparation 2011)
- Depperschmidt, A., Greven A.,Pfaffelhuber P.,
Tree-valued Fleming-Viot dynamics with selection,
(submitted to Annals of Probability 2011)
- Eckhoff, M., Greven A.,
Comparison techniques for multi-dimensional interacting diffusions,
(In preparation 2011)
- Geiger, J., Greven, A.,
The spatial structure of the historical process of Branching Random Walk
(In preparation 2011)
- Greven, A., Hochberg, K.,
The longtime behavior of Multilevel Branching Systems,
(In preparation 2011)
- Greven A., Klimovsky A.,
Renormalization of interacting diffusions on $\Z^2$,
(In preparation 2011)
- Greven A., Klimovsky A., Winter A.,
Tree-valued Cannings dynamics
(In preparation 2011)
- Greven A., Limic, V., Winter A.,
Cluster formation in spatial Moran models in critical dimension via particle representation,
(submitted to EJP, in revision 2010)
- Greven A., Limic, V., Winter A.,
Cluster formation in Moran models on two-dimensional tori
(In preparation 2011)
- Greven A., Pfaffelhuber P., Wakolbinger A.,
Genetic hitchhiking in substructured populations,
(In preparation 2011)
- 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)
- Greven A., Pfaffelhuber P., Sturm A., Winter A., Zähle I.,
A multitype spatial branching model for local self-regulation,
(In preparation 2011)
- Greven A., Popovic L., Winter A.,
Genealogical forests of catalytic branching random walks in the diffusion limit,
(In preparation 2011)
- Greven A., Sun R., Winter A.,
Limit genealogies of interacting Fleming-Viot processes on $\Z^1$,
(In preparation 2011)


