Conductance of a Subdiffusive Random Weighted Tree

Abstract: We build a random tree with random weights on its edges. These weights are used to define a random walk (in a random environment) on the vertices of the tree. That is a lot of randomness! But do not worry too much, the tools we use here are mostly analytical (and often elementary). Associated to this random walk is an electrical network formalism: each edge has an electrical conductance (the inverse of its resistance) and we may consider the effective conductance between the root of the tree and its $n$-th level. In the regime we are interested in (called "subdiffusive"), this conductance decreases almost surely to $0$ as $n$ goes to infinity and we will try (and not completely succeed!) to compute an almost sure equivalent of this conductance.

combinatoricscomplex variablesfunctional analysisgeneral mathematicsgroup theoryK-theory and homologynumber theoryoperator algebrasprobabilityquantum algebrarings and algebrasrepresentation theory

Audience: general audience

Comments: The password to join the talk is the order of the alternating group $A_7$.

GAG seminar

Series comments: Description: Non-specialized research seminar