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Nicholas Georgiou

Research: Probability theory; probabilitistic models and stochastic processes; (random) processes on (random) graphs; probabilistic combinatorics

Recent talks:


Other research interests:

  • Approximation and mixing times in the ferromagnetic Potts model, research with Magnus Bordewich (originally funded by his EPSRC grant). The project was focussed on Markov chain Monte Carlo techniques, the mixing time of Glauber dynamics and the approximability of the partition function of the Potts model. One topic we investigated was the negative correlation of forests, and whether this property could be used to create an efficient sampling/counting algorithm for the associated partition function.
  • Antichains in the k-dimensional random order, collaborative research project with Ed Crane. We held a related workshop in July 2011, funded by the Bristol Mathematics department’s GRASP initiative, attended by Cedric Boutillier, Graham Brightwell, Malwina Luczak and Peter Winkler.
  • Subcritically indecomposable graphs and reconstruction, collaborative research with Robert Brignall. We’re investigating the structure of indecomposable graphs (where indecomposable means with respect to modular decomposition) that have the property that very few of the vertex-deleted subgraphs (subgraphs obtained by deleting a single vertex) are indecomposable.

My thesis, Random Structures for Partially Ordered Sets, comprises two parts: in the first I studied random models that produce partial orders sequentially; in the second I studied a correlation of embeddings of rooted trees. The main results were subsequently published in my first two papers, and one section was expanded on in my “Continuum limits…” paper with Graham Brightwell, my PhD supervisor.