Kommende Veranstaltungen

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kollwit

Matthias Löwe, WWU: A short introduction into spin models in statistical mechanics (Mini-course: Spin models in statistical mechanics and Gaussian free fields, 1st and 2nd lecture)

Wednesday, 19.01.2022 16:00 per ZOOM: 61828242813

Mathematik und Informatik

Spin models in statistical mechanics have a history of almost one hundred years. They first occurred as models of ferromagnetism and Ernest Ising's PhD thesis. In this minicourse we will start with a brief survey of some results in the Ising model. We will then turn to its mean-field version the Curie-Weiss model and see how phase transition can be proved there. In a final step we will introduce some simple models of so-called spin glasses and discuss some of the results that have been proved in this context.



Angelegt am Monday, 17.01.2022 13:38 von kollwit
Geändert am Monday, 17.01.2022 13:38 von kollwit
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Oberseminare und sonstige Vorträge
Stochastik
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kollwit

Matthias Löwe, WWU: A short introduction into spin models in statistical mechanics (Mini-course: Spin models in statistical mechanics and Gaussian free fields, 3rd lecture)

Wednesday, 26.01.2022 16:00 per ZOOM: 61828242813

Mathematik und Informatik

Spin models in statistical mechanics have a history of almost one hundred years. They first occurred as models of ferromagnetism and Ernest Ising's PhD thesis. In this minicourse we will start with a brief survey of some results in the Ising model. We will then turn to its mean-field version the Curie-Weiss model and see how phase transition can be proved there. In a final step we will introduce some simple models of so-called spin glasses and discuss some of the results that have been proved in this context.



Angelegt am Monday, 17.01.2022 13:43 von kollwit
Geändert am Monday, 17.01.2022 13:43 von kollwit
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Oberseminare und sonstige Vorträge
Stochastik
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kollwit

Anita Behme, TU Dresden: Generalized Ornstein-Uhlenbeck processes in a Markov-switching environment (Oberseminar Mathematische Stochastik)

Wednesday, 26.01.2022 17:00 im Raum SRZ 216

Mathematik und Informatik

By embedding a Markov-modulated random recurrence equation in continuous time, in this talk I will derive the Markov-modulated generalized Ornstein-Uhlenbeck process. This process turns out to be the unique solution of a stochastic differential equation driven by a bivariate Markov-additive process that will be presented and solved explicitely. Afterwards we discuss basic properties of the obtained processes such as stationarity conditions and some moments. If time permits, we may also discuss a possible application and introduce a Markov-modulated risk model with investment that generalizes Paulsen?s risk process to a Markov-switching environment.



Angelegt am Wednesday, 13.10.2021 10:15 von kollwit
Geändert am Wednesday, 19.01.2022 14:00 von kollwit
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Stochastik
Oberseminare und sonstige Vorträge