Paul Smith
CNPq Postdoctoral Research Fellow
Instituto de Matemática Pura e Aplicada
Rio de Janeiro, Brasil
first initial last name at impa dot br
Research + Background
I am interested in problems in all areas of probabilistic combinatorics, random graphs, discrete probability and percolation, especially those with a connection to statistical physics.
Before returning to IMPA in 2017, I was a Postdoctoral Research Fellow at Tel Aviv University from 2016 to 2017, a Fellow and College Lecturer at Murray Edwards College, Cambridge from 2014 to 2016, and a CNPq Postdoctoral Research Fellow (for the first time) at IMPA from 2012 to 2014. I did my PhD under the supervision of Béla Bollobás in Cambridge, at Trinity College, where I was also an undergraduate.
Papers

The sharp threshold for the Duarte model
 with Béla Bollobás, Hugo DuminilCopin, and Robert Morris
 To appear, Ann. Probab.  arXiv

Nucleation and growth in two dimensions
 with Béla Bollobás, Simon Griffiths, Robert Morris, and Leonardo Rolla
 Preprint  arXiv

The threshold for jigsaw percolation on random graphs

Universality of twodimensional critical cellular automata
 with Béla Bollobás, Hugo DuminilCopin, and Robert Morris
 To appear, Proc. Lond. Math. Soc.  arXiv

Subcritical Ubootstrap percolation models have nontrivial phase transitions

The sharp threshold for maximumsize sumfree subsets in evenorder abelian groups

The time of bootstrap percolation in two dimensions

The time of bootstrap percolation with dense initial sets for all thresholds

The time of bootstrap percolation with dense initial sets

Monotone cellular automata in a random environment
Simulations
Here are some simulations of four twodimensional monotone cellular automata in a random environment: the classical twoneighbour bootstrap percolation model and the Duarte model (which are both critical, in the language of this paper), the subcritical directed triangular bootstrap percolation (DTBP) model (see this paper on subcritical models), and a toy supercritical model. The precise defintion of each model is given on the simulations homepage.
The simulator runs the models on 300 x 300 tori and may be modified by changing the values of the variables in the query string: density is what you think it is; type refers to the model; rate is the number of sites that are updated in each new frame. The simulator was written in Javascript / jQuery by Alex Holyoake, to whom I am greatly indebted.
Talk
In July 2016, I gave a talk at the Isaac Newton Institute in Cambridge, entitled ‘Towards universality in bootstrap percolation’. That talk may be viewed online.
Nespresso Index
I have put together a comparison of the prices of Nespresso capsules around the world.