Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Abstract: A natural classification of random walks is the one into recurrent and transient ones. This is equivalent to the non-/validity of the Hardy inequality for the energy functional associated with the Laplace operator on the graph. The latter is an abstract inequality between functionals and can be generalised further. In this talk, we discuss a generalisation to the quasi-linear setting and show a method to get optimal Hardy weights. We illustrate this method on the natural numbers and on regular trees. If the time permits, we also discuss characterisations of having a Hardy inequality.
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