Session S06 - Interacting Stochastic Systems

Tuesday, July 13, 14:50 ~ 15:25 UTC-3

Stochastic recursions on directed random graphs

Mariana Olvera-Cravioto

University of North Carolina at Chapel Hill, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We study a family of Markov processes on directed graphs where the values at each vertex are influenced by the values of its inbound neighbors and by independent fluctuations either on the vertices themselves or on the edges connecting them to their inbound neighbors. Typical examples include PageRank, the generalized deGroot model, and other information propagation processes on directed graphs. Assuming a stationary distribution exists for this Markov chain, our goal is to characterize the marginal distribution of a uniformly chosen vertex in the graph. In order to obtain a meaningful characterization, we assume that the underlying graph converges in the local weak sense to a marked Galton-Watson process, e.g., a directed configuration model or any rank-1 inhomogeneous random digraph. We then prove that the stationary distribution we study on the graph converges in a Wasserstein metric to a distribution characterized through a branching distributional fixed-point equation and its endogenous solution.

Joint work with Tzu-Chi Lin (University of North Carolina at Chapel Hill) and Nicolás Fraiman (University of North Carolina at Chapel Hill).

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