Bela Bollobas - Selected Publications#


The time of bootstrap percolation in two dimensions, Probab. Theory Related Fields 166 (2016), 321-364. (with P. Balister and P. Smith)

Subcritical U-bootstrap percolation models have non-trivial phase transitions, Trans. Amer. Math. Soc. 368 (2016), 7385-7411. (with P. Balister, M. Przkucki and P. Smith)

Monotone cellular automata in a random environment, Combin. Probab. Comput. 24 (2015), 687-722. (with P. Smith and A. Uzzell)

The sharp threshold for bootstrap percolation in all dimensions, Trans. Amer. Math. Soc. 364 (2012), 2667-2701. (with J. Balogh, H. Duminil-Copin and R. Morris)

Projections, entropy and sumsets, Combinatorica 32 (2012), 125-141. (with P. Balister)

Bootstrap percolation in high dimensions, Combin. Probab. Comput. 19 (2010), 643-692. (with J. Balogh and R. Morris)

The phase transition in inhomogeneous random graphs, Random Structures and Algorithms 31 (2007), 3-122. (with S. Janson and O. Riordan)

The critical probability for random Voronoi percolation in the plane is 1/2, Probab. Theory Related Fields 136,
(2006), 417-468. (with O. Riordan)

A two-variable interlace polynomial, Combinatorica 24 (2004), 567-584.

A polynomial of graphs on surfaces, Math. Ann. 323 (2002), 81-96. (with O. Riordan)


Remarks. As Bollobas has had over 450 publications and has worked in several areas, a selection of 10 papers cannot come close to showing the impact of his work.

The novel polynomials introduced in 9 and 10, the two-variable interlace polynomial and the Bollobas-Riordan polynomial, have had plenty of reverberations in mathematics and physics.

In 8, new methods were introduced to determine the critical probability of random Voronoi percolation in the plane: a much deeper exact result than the critical probability of percolation on the square lattice.

In 7, a general model of inhomogeneous random graphs was defined, incorporating a large family of earlier models. In spite of the generality of this model, precise results were proved about the phase transition in the model.

Papers 4 and 6 are only two of the many publications on the critical probability of `classical' bootstrap percolation. The results obtained had been considered to be out of range by most experts.

In 3, monotone cellular automata are introduced with totally general update rules. Amazingly, there is a rough classification of these general cellular automata into three types, with very different critical probabilities. This study was continued in 1 and 2, and in several manuscripts. There is no doubt that this is the beginning of a huge and very difficult theory.

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