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Dear Participants,
Lecture 07 is uploaded to the web page and you can download it by clicking on the PDF link
https://www.mat.tuhh.de/veranstaltungen/isem26/_media/lecture07.pdf
This week, we focus on an approximation property. Namely, approximating an infinite graph by a sequence of finite graphs, we study how the corresponding Dirichlet forms and Laplacians behave. We will also provide a general perspective on Dirichlet forms and the Markov property. Note that regular Dirichlet forms and the corresponding semigroups give rise to Markov processes, and there is a one-to-one correspondence between these objects. Thus, regular Dirichlet forms and semigroups provide an analytic framework to study (properties of) this class of stochastic processes. We do not go into details here, but rather focus on further analytical properties of our graphs and associated objects which, however, can also be interpreted in the world of stochastic processes.
We kindly ask the team of Hamburg to provide solutions to the exercises for this lecture.
With the best regards,
your virtual lecturers.
