December 12, 2014Location: Janskerkhof 15a (Utrecht), room 101
We extend classical pyramidal algorithms of signal processing on the torus to the case of generic weighted graphs. This is done by making a connection with “local equilibria” appearing in the Diaconis and Fill intertwining relation. This connection actually provides a way to identify local equilibria of generic Markov chains starting from the adaptation, through random spanning forests, of the classical subsampling procedure of signal processing.
This is work in progress with Luca Avena, Fabienne Castell and Clothilde Mélot.
A point process is R-independent, if it behaves independently on subspaces lying at least distance R apart from each other. We discuss the common structure of this class of point processes, in particular uniform control of the avoidance probabilities and stochastic domination. A key role is played by the unique R-independent point process with an R-hardcore, which also has a surprising connection with the hard-sphere model with radius R. This leads to a discussion of cluster expansions of Markov point processes and possible deeper connections between R-independent point processes and Markov point processes.