University of Cambridge > > Probability > Random lattice triangulations

Random lattice triangulations

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact clc32.

We consider lattice triangulations as triangulations of the integer points in the square [0; n]x[0; n]. Our focus is on random triangulations in which the probability of obtaining a given lattice triangulation T is proportional to \lambda^|T|, where \lambda is a positive real parameter and |T| is the total length of the edges in T. Empirically, this model exhibits a phase transition at \lambda = 1 (corresponding to the uniform distribution): for \lambda < 1 distant edges behave essentially independently, while for \lambda > 1 very large regions of aligned edges appear. We substantiate this picture as follows. For \lambda < 1 sufficiently small, we show that correlations between edges decay exponentially with distance (suitably de fined), and also that the Glauber dynamics (a local Markov chain based on flipping edges) is rapidly mixing (in time polynomial in the number of edges in the triangulation). By contrast, for \lambda > 1 we show that the mixing time is exponential. Joint work with Pietro Caputo, Fabio Martinelli and Alistair Sinclair.

This talk is part of the Probability series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2024, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity