08.10.2024, 10:15 - 11:45
– 3.06.H02
Kálmán Lecture
Particle Methods in Machine Learning and Inverse Problems
Martin Burger, Helmholtz Imaging
Alexander Zass (UP)
In this talk we present some results on the existence and uniqueness of marked Gibbs point processes. Firstly, we prove in a general setting the existence of an infinite-volume marked Gibbs point process, via the so-called entropy method from large deviations theory. We then adapt it to the setting of infinite-dimen-sional Langevin diffusions, put in interaction via a Gibbsian description; we also obtain the uniqueness of such a Gibbs process via cluster expansion techniques. Finally, we explore the question of uniqueness in the case of repulsive interactions, in a novel approach to uniqueness by applying the discrete Dobrushin criterion to the continuum framework.
Zoom-access is available on
www.math.uni-potsdam.de/fileadmin/user_upload/Prof-Wahr/Roelly/FS_21.pdf