Seminar on stochastic processes: Dynamic random graphs

Lecturer:

Course typ:

Seminar

Description:

A static random graph consists of a number n of vertices (also called nodes) that are connected by edges. Here, the number of vertices n is fixed and is generally assumed to be large. Mathematically, we are in particular interested in the asymptotic properties of the random graph as n → ∞. The randomness of the graph stems from the fact that whether an edge between two vertices is present or not is given by a (Bernoulli) random variable. We distinguish static and dynamic random graph models. In static random graph models we study a graph of a given size n while in dynamic random graph models we are (also) interested in the (random) growth of a network to a given size n as well as the dynamics over time, particularly if the number of nodes may also decrease and their connectivity may change over time. A special case that we will give particular attention to if given by random trees, which are random graphs without so called loops.

Random graphs are models for real life complex networks. The vertices represent the entities of the network, the edges some relationship between these edges. Such networks are ubiquitous in today"s world: Social networks, computer networks, telephone networks to name just a few important ones. It is thus a very active area of applied probability theory to come up with realistic random graph models and to study the structure and properties of these random objects regarding for example the spread of diseases, routing information, and ranking of the vertices present. One also wants to understand which networks have similar features and why this is the case.

Literatur:
The main literature for the seminar will be the book Random graphs and complex networks by Remco van der Hofstad which can be found online under https://www.win.tue.nl/∼rhofstad/NotesRGCN.pdf

Place:

(Raum 5.101 Seminarraum: Goldschmidtstr. 7 (Informatik u.Stochastik), Gebaeude Informatik/Stochastik)

Semester:

WiSe 2019/20

Times:

Tue.. 14:15 - 15:45 (weekly), Dates on Sunday, 10.11.2019 (all-day)
First appointment: Tuesday, 22.10.2019 14:15 - 15:45, Room: (Raum 5.101 Seminarraum: Goldschmidtstr. 7 (Informatik u.Stochastik), Gebaeude Informatik/Stochastik)

Course number:

502780

Pre-requisites:

For participation in the seminar basic knowledge of probability theory and stochastic processes is needed that you would have acquired in the lecture "Mass- und Wahrscheinlichkeitstheorie"as well as in the introductory lecture of the cycle "Stochastic Processes". Knowledge of respectively participation in the second and third part of the cycle may sometimes be helpful but is not essential.

Learning organisation:

The preferred language of the seminar will be English. However, talks may be presented in German.

Area classification:

Vorlesungsverzeichnis WiSe 2019/2020 > Fakultät für Mathematik und Informatik > Lehrveranstaltungen der Lehreinheit Mathematik > Masterstudiengang Mathematik (M.Sc.) > Studienprofil W "Wirtschaftsmathematik" > (Ober-)Seminare in SP 3 & SP 4
Vorlesungsverzeichnis WiSe 2019/2020 > Fakultät für Mathematik und Informatik > Lehrveranstaltungen der Lehreinheit Mathematik > Masterstudiengang Mathematik (M.Sc.) > Studienprofil W "Wirtschaftsmathematik" > Wahlmodule SP 1 - 4
Vorlesungsverzeichnis WiSe 2019/2020 > Fakultät für Mathematik und Informatik > Lehrveranstaltungen der Lehreinheit Mathematik > Masterstudiengang Mathematik (M.Sc.) > Studienprofil W "Wirtschaftsmathematik" > Wahlpflichtmodule SP 4
Vorlesungsverzeichnis WiSe 2019/2020 > Fakultät für Mathematik und Informatik > Lehrveranstaltungen der Lehreinheit Mathematik > Masterstudiengang Mathematik (M.Sc.) > Studienprofil F "Forschungsorientiert - allgemein" > Mathematische Module SP 4
Vorlesungsverzeichnis WiSe 2019/2020 > 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 2019/2020 > Fakultät für Mathematik und Informatik > Lehrveranstaltungen der Lehreinheit Mathematik > Masterstudiengang Mathematik (M.Sc.) > Studienprofil Phy "Physik" > Wahlmodule SP 4
Vorlesungsverzeichnis WiSe 2019/2020 > Fakultät für Mathematik und Informatik > Lehrveranstaltungen der Lehreinheit Mathematik > Masterstudiengang Mathematik (M.Sc.) > Studienprofil Phy "Physik" > Wahlpflichtmodule SP 4

Further information from Stud.IP about this course

Home institute: Bereich Mathematik
Participating institute: Institut für Mathematische Stochastik
Participants registered in Stud.IP: 12
Number of postings in Stud.IP forum: 2
Number of documents in the Stud.IP download area: 1