PNA Colloquium

     		-  P N A    C O L L O Q U I U M  -  

 


		        Thursday May 19, 2005



                                 by



                            Rachel Brouwer



                 Self-organised critical forest fires


Forest-fires models are believed to display self-organised critical 
behaviour. Unfortunately, most results in this area are non-rigorous 
and in many cases based on computer simulations. The question is 
however, how much of this can be proved rigorously. This talk firstly 
discusses self-destructive percolation, which has close relations with 
forest-fire models: consider ordinary site percolation on an infinite 
graph in which the sites, independent of each other, are occupied with 
probability p and vacant with probability 1-p. Now suppose that, by 
some catastrophe, all sites which are in an infinite occupied cluster 
become vacant. Finally, each site that is vacant after the catastrophe,
becomes occupied with probability d, independent of the other sites.
One would expect that if p is larger (but very close to) the critical 
value, that after the removal of the infinite cluster, a very small 
value of d is needed to create an infinite cluster in the final 
configuration. On the binary tree this is indeed the case. However, 
we conjecture that on the square lattice, this intuition is not true. 
We will show that the conjecture, if it is true, has some remarkable 
consequences, not only for the self-destructive percolation model, but 
also for the forest-fire model.


Time:	 4pm
Place:	 CWI, Kruislaan 413, 1098 SJ Amsterdam
Room:	 M280
Info:	 Marie-Colette van Lieshout 
	 tel: 020 5924008 
	 http://www.cwi.nl/~colette/pna.html