Anita Kollwitz

Anna Muranova, Olsztyn, Poland: Recurrence and transience of generalized networks (Oberseminar Mathematische Stochastik)

Wednesday, 13.07.2022 17:00 im Raum M4

Mathematik und Informatik

It is known that weighted graphs can be considered as electrical networks with resistors (in this case weights are called conductances). If we generalize settings and add inductors and capacitors to networks, then admittance is the generalization of conductance and it is a positive real rational function on complex parameter s. We introduce the admittance operator $P_s$, which acts on functions $f: V\to \mathbb{C}$ and is a Markov operator (or transition matrix) for any $s>0$. We analyse the analogues of the different Laplace type equations associated with $P_s$ when s is complex, as compared to the well-understood case when it is real. Moreover, we relate the Green function, resp. the analogues of escape probabilities, with the effective admittance of infinite electrical network. Then we prove that the notion of transience/recurrence does not depend on the parameter s, from where new result for random walk on graphs follows.

Angelegt am Monday, 30.05.2022 17:27 von Anita Kollwitz
Geändert am Monday, 30.05.2022 17:27 von Anita Kollwitz
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