Existence and representation problems in discrete stationary processes

Dr. Christoph Hofer-Temmel

Abstract:

A process is stationary, if its law is invariant under a time shift. Well known examples of stationary processes are iid process, Markov chains, Gibbs ensembles and block-factor constructions. A classic question are the search for necessary and sufficient conditions to represent a general stationary process as simple constructs of the above basic processes. First, I review the problem of lumpability, i.e., representing a stationary process by a deterministic coordinate-wise projection of a Markov chain (this may be seen as a special case of a hidden Markov model). Second, I review recent work by Holroyd et al on one-dependent colorings of the integers, involving factors of Bernoulli. Finally, I turn to one-color marginals and binary one-dependent processes, where stochastic domination enters the game.

Biography:

Christoph Hofer-Temmel studied mathematics at the TU Graz and Aix-Marseille Université. He defended his PhD about Bernoulli random fields and applications in percolation theory and statistical mechanics in 2012. Afterwards he spent 2 years as a postdoc at the VU Amsterdam and is since 2015 assistant professor at the NLDA in Den Helder. His current research centers around point processes and stochastic domination in the context of percolation and statistical-mechanical models and lumpings and entropy of stochastic processes.