State classification for a class of interacting superprocesses with location dependent branching.
Wang, Hao (2002)
Electronic Communications in Probability [electronic only]
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Wang, Hao (2002)
Electronic Communications in Probability [electronic only]
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Emmanuel Cépa, Dominique Lépingle (2001)
ESAIM: Probability and Statistics
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The brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices is interpreted as a system of interacting brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). We prove that...
Bertoin, Jean, Gnedin, Alexander V. (2004)
Electronic Journal of Probability [electronic only]
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Dawson, Donald A., Etheridge, Alison M., Fleischmann, Klaus, Mytnik, Leonid, Perkins, Edwin A., Xiong, Jie (2002)
Electronic Journal of Probability [electronic only]
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Harris, John William, Harris, Simon C. (2007)
Electronic Communications in Probability [electronic only]
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J. W. Harris, S. C. Harris, A. E. Kyprianou (2006)
Annales de l'I.H.P. Probabilités et statistiques
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David Dereudre (2003)
ESAIM: Probability and Statistics
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In this paper, we prove that the laws of interacting brownian particles are characterized as Gibbs fields on pathspace associated to an explicit class of hamiltonian functionals. More generally, we show that a large class of Gibbs fields on pathspace corresponds to brownian diffusions. Some applications to time reversal in the stationary and non stationary case are presented.
Kurkova, I., Popov, S., Vachkovskaia, M. (2004)
Electronic Journal of Probability [electronic only]
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Xiong, Jie (2004)
Electronic Communications in Probability [electronic only]
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Engländer, János (2007)
Probability Surveys [electronic only]
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Birkner, Matthias, Blath, Jochen (2009)
Electronic Journal of Probability [electronic only]
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