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Seminar on Gibbs point processes
Lecturer:
Prof. Dr. Dominic Schuhmacher
Course typ:
Seminar
Description:
Gibbs point processes are random point configurations on R^d (more rigorously: random locally finite
counting measures) whose conditional probability distributions on bounded sets are specified via an
"energy function" that typically depends on geometric properties of the configuration.
Gibbs processes have a long standing history in statistical physics, where they model large systems
of small particles (e.g. molecules) and thus explain among other things different phases and their
transitions. Since at least the 1980ies they have also been studied in the context of probability theory
and statistics. Here Gibbs point processes have been used to model a plethora of phenomena, from cell
structures, over trees in a forest, spatial locations of disease cases and epicentres of earthquakes, up to
galaxies. Both mathematical properties of Gibbs processes (existence/uniqueness results, formulae for
moment measures, limit theorems) and their statistical properties (asymptotic behaviour of various
estimators and algorithmic/numerical problems) are of interest.
While the exchange of knowledge about Gibbs processes between statistical physics and stochastics is
increasing, there are still many results from one field not commonly known in the other one. In the
courses Spatial Stochastics II (this semester) and III we treat Gibbs point processes quite extensively
from the point of view of probability and statistics. But we will not be able to look at many of the
intuitions, proof techniques and computational tricks known in statistical physics.
The present seminar complements the course (but may also be followed independently) by building up the theory of Gibbs processes from their basics using standard conventions and notation from probability theory, but taking a statistical physics point of view.





Literatur:
We follow the lecture notes
Sabine Jansen (2018). Gibbsian Point Processes, LMU Munich.
Available at http://www.mathematik.uni-muenchen.de/~jansen/gibbspp.pdf
Place:
(Raum 5.101 Seminarraum: Goldschmidtstr. 7 (Informatik u.Stochastik), Gebaeude Informatik/Stochastik)
Semester:
WiSe 2018/19
Times:
Tue.. 16:15 - 17:45 (weekly), Dates on Tuesday. 09.10. 16:15 - 17:45, Sunday. 04.11. (all-day)
Preliminary discussion: Tue , 09.10.2018 16:15 - 17:45
First appointment: Tue , 09.10.2018 16:15 - 17:45, Room: (Raum 5.101 Seminarraum: Goldschmidtstr. 7 (Informatik u.Stochastik), Gebaeude Informatik/Stochastik)
Course number:
502406
Participants:
Bachelor and Master students of mathematics, from 5th semester Bachelor or 1st semester Master Students are encouraged to give their talks in English.
Pre-requisites:
Measure and probability theory and another probability theory lecture (Stochastics or the first part of a cycle). In addition it is highly recommended that you fall into at least one of the following categories: (1) You are following the lecture Spatial Stochastics II in parallel; (2) You have attended a seminar or lecture on point processes in a previous semester; (3) You have some previous knowledge of statistical physics.
Area classification:
Vorlesungsverzeichnis WiSe 2018/2019 > Fakultät für Mathematik und Informatik > Lehrveranstaltungen der Lehreinheit Mathematik > Bachelorstudiengang Mathematik (B.Sc.) > Weiterführende mathematische Module in Zyklen im SP 4 (ab 5. Semester)
Vorlesungsverzeichnis WiSe 2018/2019 > Fakultät für Mathematik und Informatik > Lehrveranstaltungen der Lehreinheit Mathematik > Masterstudiengang Mathematik (M.Sc.) > Studienprofil Phy "Physik" > Wahlmodule SP 4
Vorlesungsverzeichnis WiSe 2018/2019 > Fakultät für Mathematik und Informatik > Lehrveranstaltungen der Lehreinheit Mathematik > Masterstudiengang Mathematik (M.Sc.) > Studienprofil Phy "Physik" > Wahlpflichtmodule SP 4
Vorlesungsverzeichnis WiSe 2018/2019 > Fakultät für Mathematik und Informatik > Lehrveranstaltungen der Lehreinheit Mathematik > Masterstudiengang Mathematik (M.Sc.) > Studienprofil W "Wirtschaftsmathematik" > Wahlmodule SP 1 - 4
Vorlesungsverzeichnis WiSe 2018/2019 > Fakultät für Mathematik und Informatik > Lehrveranstaltungen der Lehreinheit Mathematik > Masterstudiengang Mathematik (M.Sc.) > Studienprofil W "Wirtschaftsmathematik" > Wahlpflichtmodule SP 4
Vorlesungsverzeichnis WiSe 2018/2019 > Fakultät für Mathematik und Informatik > Lehrveranstaltungen der Lehreinheit Informatik > Master-Studiengang Angewandte Informatik > Angewandte Informatik > Wissenschaftliches Rechnen
Vorlesungsverzeichnis WiSe 2018/2019 > Fakultät für Mathematik und Informatik > Lehrveranstaltungen der Lehreinheit Mathematik > Masterstudiengang Mathematik (M.Sc.) > Studienprofil F "Forschungsorientiert - allgemein" > Mathematische Module SP 4
Further information from Stud.IP about this course
Home institute: Institut für Mathematische Stochastik
Participants registered in Stud.IP: 14
Number of postings in Stud.IP forum: 2
Number of documents in the Stud.IP download area: 2